Paul Goulart - Academia.edu (original) (raw)

Papers by Paul Goulart

2014 American Control Conference, 2014

ABSTRACT Randomized optimization is a recently established tool for control design with modulated... more ABSTRACT Randomized optimization is a recently established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable for a certain class of non-convex problems, but they usually are conservative in terms of performance and are computationally demanding. In this paper, we present a novel scenario approach for a wide class of random non-convex programs. We provide a sample complexity similar to the one for uncertain convex programs, but valid for all feasible solutions inside a set of a-priori chosen complexity. Our scenario approach applies to many non-convex control-design problems, for instance control synthesis based on uncertain bilinear matrix inequalities.

2015 European Control Conference (ECC), 2015

52nd IEEE Conference on Decision and Control, 2013

IEEE Transactions on Automatic Control, 2014

ABSTRACT We propose a new method for solving chance constrained optimization problems that lies b... more ABSTRACT We propose a new method for solving chance constrained optimization problems that lies between robust optimization and scenario-based methods. Our method does not require prior knowledge of the underlying probability distribution as in robust optimization methods, nor is it based entirely on randomization as in the scenario approach. It instead involves solving a robust optimization problem with bounded uncertainty, where the uncertainty bounds are randomized and are computed using the scenario approach. To guarantee that the resulting robust problem is solvable we impose certain assumptions on the dependency of the constraint functions with respect to the uncertainty and show that tractability is ensured for a wide class of systems. Our results lead immediately to guidelines under which the proposed methodology or the scenario approach is preferable in terms of providing less conservative guarantees or reducing the computational cost.

Proceedings of the 19th IFAC World Congress, 2014

IEEE Transactions on Automatic Control, 2015

2014 European Control Conference (ECC), 2014

ABSTRACT We consider Stochastic Model Predictive Control (SMPC) for constrained linear systems wi... more ABSTRACT We consider Stochastic Model Predictive Control (SMPC) for constrained linear systems with additive disturbance, under affine disturbance feedback (ADF) policies. One approach to solve the chance-constrained optimization problem associated with the SMPC formulation is randomization, where the chance constraints are replaced by a number of sampled hard constraints, each corresponding to a disturbance realization. The ADF formulation leads to a quadratic growth in the number of decision variables with respect to the prediction horizon, which results in a quadratic growth in the sample size. This leads to computationally expensive problems with solutions that are conservative in terms of both cost and violation probability. We address these limitations by establishing a bound on the sample size which scales linearly in the prediction horizon. The new bound is obtained by explicitly computing the maximum number of active constraints, leading to significant advantages both in terms of computational time and conservatism of the solution. The efficacy of the new bound relative to the existing one is demonstrated on a building climate control case study.

The "scenario approach" provides an intuitive method to address chance constrained problems arisi... more The "scenario approach" provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (scenarios). The sample size critically depends on Helly's dimension, a quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly's dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback. The efficacy of the proposed bound is demonstrated on an inventory management example.

2014 American Control Conference, 2014

ABSTRACT Randomized optimization is a recently established tool for control design with modulated... more ABSTRACT Randomized optimization is a recently established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable for a certain class of non-convex problems, but they usually are conservative in terms of performance and are computationally demanding. In this paper, we present a novel scenario approach for a wide class of random non-convex programs. We provide a sample complexity similar to the one for uncertain convex programs, but valid for all feasible solutions inside a set of a-priori chosen complexity. Our scenario approach applies to many non-convex control-design problems, for instance control synthesis based on uncertain bilinear matrix inequalities.

Proceedings of the 19th IFAC World Congress, 2014

Page 1. AN EFFICIENT DECOMPOSITION-BASED FORMULATION FOR ROBUST CONTROL WITH CONSTRAINTS Paul J. ... more Page 1. AN EFFICIENT DECOMPOSITION-BASED FORMULATION FOR ROBUST CONTROL WITH CONSTRAINTS Paul J. Goulart ∗ Eric C. Kerrigan ∗ ∗ Department of Engineering, University of Cambridge, Trumpington ...

Computing Research Repository, 2011

This paper introduces a new method for proving global stability of fluid flows through the constr... more This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a Lyapunov function. We then show how these methods can be extended to full infinite dimensional Navier-Stokes systems

In this paper we present a new method for assessing the stability of finite-dimensional approxima... more In this paper we present a new method for assessing the stability of finite-dimensional approximations to the Navier-Stokes equation for fluid flows. Approximations to the Navier-Stokes equation typically take the form of a set of linear ODEs with an additional bilinear term that conserves the total energy of the system state. We suggest a structured method for generating Lyapunov functions

This paper is concerned with the control of constrained linear discrete-time systems subject to b... more This paper is concerned with the control of constrained linear discrete-time systems subject to bounded state disturbances and arbitrary convex state and input con- straints. The paper employs a class of nite horizon feedback control policies parameter- ized as afne functions of the system state, calculation of which has recently been shown to be tractable via a convex reparameterization. When

This paper is concerned with the stability of a class of robust and constrained optimal control l... more This paper is concerned with the stability of a class of robust and constrained optimal control laws for linear discrete-time systems subject to bounded state dis- turbances and arbitrary convex constraints on the states and inputs. The paper considers the class of feedback control policies parameterized as ane functions of the system state, calculation of which has recently been shown

2014 American Control Conference, 2014

ABSTRACT Randomized optimization is a recently established tool for control design with modulated... more ABSTRACT Randomized optimization is a recently established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable for a certain class of non-convex problems, but they usually are conservative in terms of performance and are computationally demanding. In this paper, we present a novel scenario approach for a wide class of random non-convex programs. We provide a sample complexity similar to the one for uncertain convex programs, but valid for all feasible solutions inside a set of a-priori chosen complexity. Our scenario approach applies to many non-convex control-design problems, for instance control synthesis based on uncertain bilinear matrix inequalities.

2015 European Control Conference (ECC), 2015

52nd IEEE Conference on Decision and Control, 2013

IEEE Transactions on Automatic Control, 2014

ABSTRACT We propose a new method for solving chance constrained optimization problems that lies b... more ABSTRACT We propose a new method for solving chance constrained optimization problems that lies between robust optimization and scenario-based methods. Our method does not require prior knowledge of the underlying probability distribution as in robust optimization methods, nor is it based entirely on randomization as in the scenario approach. It instead involves solving a robust optimization problem with bounded uncertainty, where the uncertainty bounds are randomized and are computed using the scenario approach. To guarantee that the resulting robust problem is solvable we impose certain assumptions on the dependency of the constraint functions with respect to the uncertainty and show that tractability is ensured for a wide class of systems. Our results lead immediately to guidelines under which the proposed methodology or the scenario approach is preferable in terms of providing less conservative guarantees or reducing the computational cost.

Proceedings of the 19th IFAC World Congress, 2014

IEEE Transactions on Automatic Control, 2015

2014 European Control Conference (ECC), 2014

ABSTRACT We consider Stochastic Model Predictive Control (SMPC) for constrained linear systems wi... more ABSTRACT We consider Stochastic Model Predictive Control (SMPC) for constrained linear systems with additive disturbance, under affine disturbance feedback (ADF) policies. One approach to solve the chance-constrained optimization problem associated with the SMPC formulation is randomization, where the chance constraints are replaced by a number of sampled hard constraints, each corresponding to a disturbance realization. The ADF formulation leads to a quadratic growth in the number of decision variables with respect to the prediction horizon, which results in a quadratic growth in the sample size. This leads to computationally expensive problems with solutions that are conservative in terms of both cost and violation probability. We address these limitations by establishing a bound on the sample size which scales linearly in the prediction horizon. The new bound is obtained by explicitly computing the maximum number of active constraints, leading to significant advantages both in terms of computational time and conservatism of the solution. The efficacy of the new bound relative to the existing one is demonstrated on a building climate control case study.

The "scenario approach" provides an intuitive method to address chance constrained problems arisi... more The "scenario approach" provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (scenarios). The sample size critically depends on Helly's dimension, a quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly's dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback. The efficacy of the proposed bound is demonstrated on an inventory management example.

2014 American Control Conference, 2014

ABSTRACT Randomized optimization is a recently established tool for control design with modulated... more ABSTRACT Randomized optimization is a recently established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable for a certain class of non-convex problems, but they usually are conservative in terms of performance and are computationally demanding. In this paper, we present a novel scenario approach for a wide class of random non-convex programs. We provide a sample complexity similar to the one for uncertain convex programs, but valid for all feasible solutions inside a set of a-priori chosen complexity. Our scenario approach applies to many non-convex control-design problems, for instance control synthesis based on uncertain bilinear matrix inequalities.

Proceedings of the 19th IFAC World Congress, 2014

Page 1. AN EFFICIENT DECOMPOSITION-BASED FORMULATION FOR ROBUST CONTROL WITH CONSTRAINTS Paul J. ... more Page 1. AN EFFICIENT DECOMPOSITION-BASED FORMULATION FOR ROBUST CONTROL WITH CONSTRAINTS Paul J. Goulart ∗ Eric C. Kerrigan ∗ ∗ Department of Engineering, University of Cambridge, Trumpington ...

Computing Research Repository, 2011

This paper introduces a new method for proving global stability of fluid flows through the constr... more This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a Lyapunov function. We then show how these methods can be extended to full infinite dimensional Navier-Stokes systems

In this paper we present a new method for assessing the stability of finite-dimensional approxima... more In this paper we present a new method for assessing the stability of finite-dimensional approximations to the Navier-Stokes equation for fluid flows. Approximations to the Navier-Stokes equation typically take the form of a set of linear ODEs with an additional bilinear term that conserves the total energy of the system state. We suggest a structured method for generating Lyapunov functions

This paper is concerned with the control of constrained linear discrete-time systems subject to b... more This paper is concerned with the control of constrained linear discrete-time systems subject to bounded state disturbances and arbitrary convex state and input con- straints. The paper employs a class of nite horizon feedback control policies parameter- ized as afne functions of the system state, calculation of which has recently been shown to be tractable via a convex reparameterization. When

This paper is concerned with the stability of a class of robust and constrained optimal control l... more This paper is concerned with the stability of a class of robust and constrained optimal control laws for linear discrete-time systems subject to bounded state dis- turbances and arbitrary convex constraints on the states and inputs. The paper considers the class of feedback control policies parameterized as ane functions of the system state, calculation of which has recently been shown