Michael Šebek | Czech Technical University in Prague (original) (raw)
Papers by Michael Šebek
Summary: A new method of characteristic polynomial assignment for delay-differential systems, bot... more Summary: A new method of characteristic polynomial assignment for delay-differential systems, both retarded and neutral, is presented. The method consists in solving a 2-D polynomial equation. Solvability conditions well suited for a practical testing are given and the class of all assignable polynomials is parametrized. The problems of minimality, causality, properness and stabilization are discussed. The method is used to stabilize even not formally stable plants.
IFAC Proceedings Volumes, 2003
A new algebraic approach to RI-optimal control is presented in this paper. SISO case is dealt wit... more A new algebraic approach to RI-optimal control is presented in this paper. SISO case is dealt with but the proposed approach can easily be extended to one-block MIMO case. The major result is that zero and rank interpolation conditions are replaced by noncoprimeness conditions for polynomials or polynomial matrices. Constraints for the linear program are thus expressed using Sylvester matrix instead of a (possibly) ill-conditioned Vandermonde matrix.
2016 IEEE 55th Conference on Decision and Control (CDC), 2016
This paper investigates output H<sub>∞</sub> synchronization of a group of linear het... more This paper investigates output H<sub>∞</sub> synchronization of a group of linear heterogeneous agents. Agents are subject to external unmodeled disturbances and distributively communicate one set of outputs. The aim is to design a distributed controller to achieve synchronization on another set of outputs with an H<sub>∞</sub> bound. We obtain an H<sub>∞</sub>-criterion for each agent that guarantees output synchronization in the absence of the external unmodeled disturbances and output H<sub>∞</sub> synchronization in their presence. We derive the overall L<sub>2</sub>-gain of the output synchronization error with respect to the external unmodeled disturbances. We demonstrate our developments by a simulation example.
IFAC-PapersOnLine, 2015
This paper presents a new method for control reconfiguration of nonlinear, inputaffine systems su... more This paper presents a new method for control reconfiguration of nonlinear, inputaffine systems subject to actuator failures. For full-state linearizable systems it is shown that after the occurrence of an actuator failure the linearizing feedback has to be adapted to the failure case. In a second step, the reconfiguration of the re-linearized system can be accomplished by means of a static linear virtual actuator. An interesting observation is the fact that the faulty system stays reconfigurable as long as there is one actuator left in the faulty plant. This paper illustrates the method by considering a fluid process.
2015 IEEE Conference on Control Applications (CCA), 2015
In this paper, the task of quantized nonlinear predictive control is addressed. In such case, val... more In this paper, the task of quantized nonlinear predictive control is addressed. In such case, values of some inputs can be from a continuous interval while for the others, it is required that the optimized values belong to a countable set of discrete values. Instead of very straightforward a posteriori quantization, an alternative algorithm is developed incorporating the quantization aspects directly into the optimization routine. The newly proposed quaNPC algorithm is tested on an example of building temperature control. The results for a broad range of number of quantization steps show that (unlike the naive a posteriori quantization) the quaNPC is able to maintain the control performance close to the performance of the original continuous-valued nonlinear predictive controller and at the same time it significantly decreases the undesirable oscillations of the discrete-valued input.
IFAC-PapersOnLine, 2015
We consider an asymptotic stability of a circular system where the coupling Laplacians are differ... more We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also in path graphs.
1986 25th IEEE Conference on Decision and Control, 1986
1988., IEEE International Symposium on Circuits and Systems
Journal of the Franklin Institute, 2015
This paper investigates multi-agent system synchronization in presence of control signal delays. ... more This paper investigates multi-agent system synchronization in presence of control signal delays. Agents are assumed to be identical linear time-invariant systems, interacting on a directed graph topology, all having the same control delay. Distributed control of multi-agent systems is complicated by the fact that the communication graph topology interplays with single-agent dynamics. Here a design method based on a synchronizing region is given that decouples the design of local feedback gains from the detailed properties of graph topology. Such extension of the synchronizing region concept to agents with delays is rigorously justified. Delay-dependent synchronizing region is defined and methods are given guaranteeing its estimates. Qualitative properties of delay-dependent synchronizing regions and implications for control design are discussed. It is found that these regions are inherently bounded which restricts the graphs that allow for synchronization under delayed communication. Stronger property of exponential stability with a prescribed convergence rate is presented as a special case.
Automatica, 1991
This paper reports recent work in the theoretical development of the polynomial equation approach... more This paper reports recent work in the theoretical development of the polynomial equation approach to the optimization of multivariable control systems. The algebraic properties of the polynomial matrix equations which define the optimal controller are investigated, and new results concerned with the numerical solvability of the equations are derived. Notation-All systems considered in this paper are described by means of real polynomial matrices in the delay operator d. The reader is referred to Ku~era (1979) for details. For simplicity the arguments of polynomial matrices are often omitted, such that X(d) is denoted by X. The adjoint of X(d) is written as X*(d)=Xr(d-l). For any polynomial matrix X(d) define (X) as the matrix of terms independent of d. Stable square polynomial matrices are those with zeros of their determinant strictly outside the unit circle of the d-plane.
IFAC Proceedings Volumes, 1984
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz KYBERNETIKA-VOLUME 23 (1987), NUMBER 4 MODEL MATCHING OF 2-D MULTI-INPUT MULTI-OUTPUT SYSTEMS 1 MICHAEL ŠEBEK An analysis of the exact model matching problems of 2-D linear multi-input multi-output systems is presented. The approach is based on input-output 2-D polynomial models and all solutions to the problem are expressed in a parametric form. Compact necessary and sufficient conditions for the existence of causal and stable solutions are given. A design procedure is proposed which provides a stable causal solution. It consists essentially of solving a linear equation in 2-D polynomial matrices.
IEEE Control Systems, 2006
ABSTRACT
The paper tailors the so-called wave-based control popular in the field of flexible mechanical st... more The paper tailors the so-called wave-based control popular in the field of flexible mechanical structures to the field of distributed control of vehicular platoons. The proposed solution augments the symmetric bidirectional control algorithm with a wave-absorbing controller implemented on the leader, and/or on the rear-end vehicle. The wave-absorbing controller actively absorbs an incoming wave of positional changes in the platoon and thus prevents oscillations of inter-vehicle distances. The proposed controller significantly improves the performance of platoon manoeuvrers such as acceleration/deceleration or changing the distances between vehicles without making the platoon string unstable. Numerical simulations show that the wave-absorbing controller performs efficiently even for platoons with a large number of vehicles, for which other platooning algorithms are inefficient or require wireless communication between vehicles.
2001 European Control Conference (ECC)
This paper studies multivariable adaptive control and parameterization issues related to polynomi... more This paper studies multivariable adaptive control and parameterization issues related to polynomial matrices. Firstly, it introduces a new scheme for discrete-time MRACS (model reference adaptive control systems) based upon recursive QR factorization. This scheme is then generalized to the continuous-time case. Finally, an issue concerning parameterization of multivariable systems is discussed in relation to polynomial matrices.
This report describes our joint work on implementation of effective numerical routines for two-va... more This report describes our joint work on implementation of effective numerical routines for two-variable polynomial matrices in the MATHEMATICA software. New functions are connected to the already created program package, being developed at the Czech Technical University in Prague, which calculates only with polynomial matrices in one variable. As the first step, new polynomial object for 2-D polynomial matrix was created in the MATHEMATICA programming language. This was essential for good integration with the polynomial package mentioned above. Implementation of a bunch of efficient and reliable numerical routines followed.
IEEE Transactions on Control Systems Technology
This paper tackles networked distributed observer 1 and controller design problem over directed g... more This paper tackles networked distributed observer 1 and controller design problem over directed graph topology for 2 spatially interconnected systems. Traditional centralized design 3 methods suffer from a lack of adaptability to graph variations 4 incurred by network reconfiguration, communication failures, 5 and redundant sensors integration. In this paper, to handle 6 the foregoing limitations imposed by centralized design, state 7 observers are designed in a distributed manner facilitated by 8 pinning control precepts. On the one hand, this novel approach 9 adds fault tolerance with respect to communication link failures. 10 On the other hand, the proposed approach brings flexibility of 11 integrating additional sensors into the network. In addition, this 12 approach affords a reduction of computational cost. A sufficient 13 condition to guarantee stability of the closed-loop system is 14 derived. The controllers, though in the end implemented in 15 a distributed way, are designed in a centralized framework, 16 where linear-quadratic-regulator theory is adopted to handle 17 the fact that separation principle fails to hold in the net-18 worked observer and controller design. Numerical simulation 19 results of a piezoelectric actuated smart flexible system are 20 presented, and the effectiveness of the proposed design is thereby 21 verified.
IEEE Transactions on Control Systems Technology
This paper focuses on the development of an optimization algorithm for car motion predictive cont... more This paper focuses on the development of an optimization algorithm for car motion predictive control that addresses both hybrid car dynamics and hybrid minimization criterion. Instead of solving computationally demanding nonlinear mixed-integer programming task or approximating the hybrid dynamics/criterion, the Hamiltonian-switching hybrid nonlinear predictive control algorithm developed in this paper incorporates the information about hybridity directly into the optimization routine. To decrease the time complexity, several adaptive prediction horizon approaches are proposed, and for some of them, it is shown that they preserve maneuverability-related properties of the car. All developed alternatives are verified on an example of a motion control of a racing car and compared with the approximation-based nonlinear predictive control and a commercial product. Moreover, a sensitivity analysis examining robustness of the algorithm is included as well.
Systems & Control Letters, 2017
The paper presents a novel approach for the analysis and control of a multi-agent system with non... more The paper presents a novel approach for the analysis and control of a multi-agent system with non-identical agents and a pathgraph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the 'local' perspective and identify the travelling waves in the multi-agent system. The local treatment of the multi-agent system is complementary to the traditional 'overall' approach. It is shown that the different dynamics of the agents creates a virtual boundary that causes a partial reflection of the travelling waves. Undesired effects due to the reflection of the waves, such as amplification/attenuation, long transient or string instability, can be compensated by the feedback controllers introduced in this paper. A set of functions in MATLAB, which allows numerical simulation of the proposed approach, have been made available on MATLAB Central.
Summary: A new method of characteristic polynomial assignment for delay-differential systems, bot... more Summary: A new method of characteristic polynomial assignment for delay-differential systems, both retarded and neutral, is presented. The method consists in solving a 2-D polynomial equation. Solvability conditions well suited for a practical testing are given and the class of all assignable polynomials is parametrized. The problems of minimality, causality, properness and stabilization are discussed. The method is used to stabilize even not formally stable plants.
IFAC Proceedings Volumes, 2003
A new algebraic approach to RI-optimal control is presented in this paper. SISO case is dealt wit... more A new algebraic approach to RI-optimal control is presented in this paper. SISO case is dealt with but the proposed approach can easily be extended to one-block MIMO case. The major result is that zero and rank interpolation conditions are replaced by noncoprimeness conditions for polynomials or polynomial matrices. Constraints for the linear program are thus expressed using Sylvester matrix instead of a (possibly) ill-conditioned Vandermonde matrix.
2016 IEEE 55th Conference on Decision and Control (CDC), 2016
This paper investigates output H<sub>∞</sub> synchronization of a group of linear het... more This paper investigates output H<sub>∞</sub> synchronization of a group of linear heterogeneous agents. Agents are subject to external unmodeled disturbances and distributively communicate one set of outputs. The aim is to design a distributed controller to achieve synchronization on another set of outputs with an H<sub>∞</sub> bound. We obtain an H<sub>∞</sub>-criterion for each agent that guarantees output synchronization in the absence of the external unmodeled disturbances and output H<sub>∞</sub> synchronization in their presence. We derive the overall L<sub>2</sub>-gain of the output synchronization error with respect to the external unmodeled disturbances. We demonstrate our developments by a simulation example.
IFAC-PapersOnLine, 2015
This paper presents a new method for control reconfiguration of nonlinear, inputaffine systems su... more This paper presents a new method for control reconfiguration of nonlinear, inputaffine systems subject to actuator failures. For full-state linearizable systems it is shown that after the occurrence of an actuator failure the linearizing feedback has to be adapted to the failure case. In a second step, the reconfiguration of the re-linearized system can be accomplished by means of a static linear virtual actuator. An interesting observation is the fact that the faulty system stays reconfigurable as long as there is one actuator left in the faulty plant. This paper illustrates the method by considering a fluid process.
2015 IEEE Conference on Control Applications (CCA), 2015
In this paper, the task of quantized nonlinear predictive control is addressed. In such case, val... more In this paper, the task of quantized nonlinear predictive control is addressed. In such case, values of some inputs can be from a continuous interval while for the others, it is required that the optimized values belong to a countable set of discrete values. Instead of very straightforward a posteriori quantization, an alternative algorithm is developed incorporating the quantization aspects directly into the optimization routine. The newly proposed quaNPC algorithm is tested on an example of building temperature control. The results for a broad range of number of quantization steps show that (unlike the naive a posteriori quantization) the quaNPC is able to maintain the control performance close to the performance of the original continuous-valued nonlinear predictive controller and at the same time it significantly decreases the undesirable oscillations of the discrete-valued input.
IFAC-PapersOnLine, 2015
We consider an asymptotic stability of a circular system where the coupling Laplacians are differ... more We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also in path graphs.
1986 25th IEEE Conference on Decision and Control, 1986
1988., IEEE International Symposium on Circuits and Systems
Journal of the Franklin Institute, 2015
This paper investigates multi-agent system synchronization in presence of control signal delays. ... more This paper investigates multi-agent system synchronization in presence of control signal delays. Agents are assumed to be identical linear time-invariant systems, interacting on a directed graph topology, all having the same control delay. Distributed control of multi-agent systems is complicated by the fact that the communication graph topology interplays with single-agent dynamics. Here a design method based on a synchronizing region is given that decouples the design of local feedback gains from the detailed properties of graph topology. Such extension of the synchronizing region concept to agents with delays is rigorously justified. Delay-dependent synchronizing region is defined and methods are given guaranteeing its estimates. Qualitative properties of delay-dependent synchronizing regions and implications for control design are discussed. It is found that these regions are inherently bounded which restricts the graphs that allow for synchronization under delayed communication. Stronger property of exponential stability with a prescribed convergence rate is presented as a special case.
Automatica, 1991
This paper reports recent work in the theoretical development of the polynomial equation approach... more This paper reports recent work in the theoretical development of the polynomial equation approach to the optimization of multivariable control systems. The algebraic properties of the polynomial matrix equations which define the optimal controller are investigated, and new results concerned with the numerical solvability of the equations are derived. Notation-All systems considered in this paper are described by means of real polynomial matrices in the delay operator d. The reader is referred to Ku~era (1979) for details. For simplicity the arguments of polynomial matrices are often omitted, such that X(d) is denoted by X. The adjoint of X(d) is written as X*(d)=Xr(d-l). For any polynomial matrix X(d) define (X) as the matrix of terms independent of d. Stable square polynomial matrices are those with zeros of their determinant strictly outside the unit circle of the d-plane.
IFAC Proceedings Volumes, 1984
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz KYBERNETIKA-VOLUME 23 (1987), NUMBER 4 MODEL MATCHING OF 2-D MULTI-INPUT MULTI-OUTPUT SYSTEMS 1 MICHAEL ŠEBEK An analysis of the exact model matching problems of 2-D linear multi-input multi-output systems is presented. The approach is based on input-output 2-D polynomial models and all solutions to the problem are expressed in a parametric form. Compact necessary and sufficient conditions for the existence of causal and stable solutions are given. A design procedure is proposed which provides a stable causal solution. It consists essentially of solving a linear equation in 2-D polynomial matrices.
IEEE Control Systems, 2006
ABSTRACT
The paper tailors the so-called wave-based control popular in the field of flexible mechanical st... more The paper tailors the so-called wave-based control popular in the field of flexible mechanical structures to the field of distributed control of vehicular platoons. The proposed solution augments the symmetric bidirectional control algorithm with a wave-absorbing controller implemented on the leader, and/or on the rear-end vehicle. The wave-absorbing controller actively absorbs an incoming wave of positional changes in the platoon and thus prevents oscillations of inter-vehicle distances. The proposed controller significantly improves the performance of platoon manoeuvrers such as acceleration/deceleration or changing the distances between vehicles without making the platoon string unstable. Numerical simulations show that the wave-absorbing controller performs efficiently even for platoons with a large number of vehicles, for which other platooning algorithms are inefficient or require wireless communication between vehicles.
2001 European Control Conference (ECC)
This paper studies multivariable adaptive control and parameterization issues related to polynomi... more This paper studies multivariable adaptive control and parameterization issues related to polynomial matrices. Firstly, it introduces a new scheme for discrete-time MRACS (model reference adaptive control systems) based upon recursive QR factorization. This scheme is then generalized to the continuous-time case. Finally, an issue concerning parameterization of multivariable systems is discussed in relation to polynomial matrices.
This report describes our joint work on implementation of effective numerical routines for two-va... more This report describes our joint work on implementation of effective numerical routines for two-variable polynomial matrices in the MATHEMATICA software. New functions are connected to the already created program package, being developed at the Czech Technical University in Prague, which calculates only with polynomial matrices in one variable. As the first step, new polynomial object for 2-D polynomial matrix was created in the MATHEMATICA programming language. This was essential for good integration with the polynomial package mentioned above. Implementation of a bunch of efficient and reliable numerical routines followed.
IEEE Transactions on Control Systems Technology
This paper tackles networked distributed observer 1 and controller design problem over directed g... more This paper tackles networked distributed observer 1 and controller design problem over directed graph topology for 2 spatially interconnected systems. Traditional centralized design 3 methods suffer from a lack of adaptability to graph variations 4 incurred by network reconfiguration, communication failures, 5 and redundant sensors integration. In this paper, to handle 6 the foregoing limitations imposed by centralized design, state 7 observers are designed in a distributed manner facilitated by 8 pinning control precepts. On the one hand, this novel approach 9 adds fault tolerance with respect to communication link failures. 10 On the other hand, the proposed approach brings flexibility of 11 integrating additional sensors into the network. In addition, this 12 approach affords a reduction of computational cost. A sufficient 13 condition to guarantee stability of the closed-loop system is 14 derived. The controllers, though in the end implemented in 15 a distributed way, are designed in a centralized framework, 16 where linear-quadratic-regulator theory is adopted to handle 17 the fact that separation principle fails to hold in the net-18 worked observer and controller design. Numerical simulation 19 results of a piezoelectric actuated smart flexible system are 20 presented, and the effectiveness of the proposed design is thereby 21 verified.
IEEE Transactions on Control Systems Technology
This paper focuses on the development of an optimization algorithm for car motion predictive cont... more This paper focuses on the development of an optimization algorithm for car motion predictive control that addresses both hybrid car dynamics and hybrid minimization criterion. Instead of solving computationally demanding nonlinear mixed-integer programming task or approximating the hybrid dynamics/criterion, the Hamiltonian-switching hybrid nonlinear predictive control algorithm developed in this paper incorporates the information about hybridity directly into the optimization routine. To decrease the time complexity, several adaptive prediction horizon approaches are proposed, and for some of them, it is shown that they preserve maneuverability-related properties of the car. All developed alternatives are verified on an example of a motion control of a racing car and compared with the approximation-based nonlinear predictive control and a commercial product. Moreover, a sensitivity analysis examining robustness of the algorithm is included as well.
Systems & Control Letters, 2017
The paper presents a novel approach for the analysis and control of a multi-agent system with non... more The paper presents a novel approach for the analysis and control of a multi-agent system with non-identical agents and a pathgraph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the 'local' perspective and identify the travelling waves in the multi-agent system. The local treatment of the multi-agent system is complementary to the traditional 'overall' approach. It is shown that the different dynamics of the agents creates a virtual boundary that causes a partial reflection of the travelling waves. Undesired effects due to the reflection of the waves, such as amplification/attenuation, long transient or string instability, can be compensated by the feedback controllers introduced in this paper. A set of functions in MATLAB, which allows numerical simulation of the proposed approach, have been made available on MATLAB Central.