Final LDRD report human interaction with complex systems: advances in hybrid reachability and control (original) (raw)
Related papers
Reachability-based abstraction for an aircraft landing under shared control
2008
We extend techniques for a reachability-based abstraction to hybrid systems under shared control with application to pilot-autopilot interaction during an aircraft landing. A simple hybrid model of longitudinal aircraft dynamics and mode-logic is developed based on publicly available data. As the pilot and autopilot share control over some of the same inputs, it is possible for the pilot to "fight" the autopilot. New types of safety are proposed to identify regions in the state-space in which pilot-autopilot conflict can occur, and then computed using level set methods. The results partition the state-space into different levels of safety. Cells of this partition form discrete modes in an abstraction of the reachability result, which can inform the design of a pilot display. Our results show how shared control contributed to violations of "safe" pilot interaction with the automation in the Nagoya 1994 A300 accident.
Composing Reachability Analyses of Hybrid Systems for Safety and Stability
Lecture Notes in Computer Science, 2010
We present a method to enhance the power of a given reachability analysis engine for hybrid systems. The method works by a new form of composition of reachability analyses, each on a different relaxation of the input hybrid system. We present preliminary experiments that indicate its practical potential for checking safety and stability.
Safe & Robust Reachability Analysis of Hybrid Systems
2017
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability - namely, the reflexive and transitive closure of a transition relation - can be unsafe, ie, it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states. Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust wrt small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exe...
Aircraft Autolander Safety Analysis Through Optimal Control-Based Reach Set Computation
Journal of Guidance, Control, and Dynamics, 2007
A method for the numerical computation of reachable sets for hybrid systems is presented and applied to the design and safety analysis of autoland systems. It is shown to be applicable to specific phases of landing: descent, flare, and touchdown. The method is based on optimal control and level set methods; it simultaneously computes a maximal controlled invariant set and a set-valued control law guaranteed to keep the aircraft within a safe set of states under autopilot mode switching. The method is applied to the sequenced flap and slat deflections of a simplified model of a DC9-30. The paper concludes with a demonstration of the method on higher dimensional aircraft models. x = state vector of the aircraft, x V; ; z z = altitude of the aircraft, m _ z 0 = maximal touchdown vertical velocity, m=s = angle of attack of the aircraft, 2 min ; max , deg = flight-path angle of the aircraft, 2 min ; max , deg = flap setting, deg = pitch of the aircraft, deg = air density, kg=m 3
Safety verification and reachability analysis for hybrid systems
Annual Reviews in Control, 2009
Safety verification and reachability analysis for hybrid systems is a very active research domain. Many approaches that seem quite different, have been proposed to solve this complex problem. This paper presents an overview of various approaches for autonomous, continuous-time hybrid systems and presents them with respect to basic problems related to verification.
A Comprehensive Method for Reachability Analysis of Uncertain Nonlinear Hybrid Systems
IEEE Transactions on Automatic Control, 2016
Reachability analysis of nonlinear uncertain hybrid systems, i.e. continuous-discrete dynamical systems whose continuous dynamics, guard sets and reset functions are defined by nonlinear functions, can be decomposed in three algorithmic steps: computing the reachable set when the system is in a given operation mode, computing the discrete transitions, i.e. detecting and localizing when (and where) the continuous flowpipe intersects the guard sets, and aggregating the multiple trajectories that result from an uncertain transition once the whole flowpipe has transitioned so that the algorithm can resume. This paper proposes a comprehensive method that provides a nicely integrated solution to the hybrid reachability problem. At the core of the method is the concept of MSPB, i.e. geometrical object obtained as the Minkowski sum of a parallelotope and an axes aligned box. MSPB are a way to control the over-approximation of the Taylor's interval integration method. As they happen to be a specific type of zonotope, they articulate perfectly with the zonotope bounding method that we propose to enclose in an optimal way the set of flowpipe trajectories generated by the transition process. The method is evaluated both theoretically by analysing its complexity and empirically by applying it to well-chosen hybrid nonlinear examples.
Reachability analysis of complex planar hybrid systems
Science of Computer Programming, 2013
Hybrid systems are systems that exhibit both discrete and continuous behavior. Reachability, the question of whether a system in one state can reach some other state, is undecidable for hybrid systems in general. The Generalized Polygonal Hybrid System (GSPDI) is a restricted form of hybrid automaton where reachability is decidable. It is limited to two continuous variables that uniquely determine which location the automaton is in, and restricted in that the discrete transitions does not allow changes in the state, only the location, of the automaton. One application of GSPDIs is for approximating control systems and verifying the safety of such systems. In this paper we present the following two contributions: i) An optimized algorithm that answers reachability questions for GSPDIs, where all cycles in the reachability graph are accelerated. ii) An algorithm by which more complex planar hybrid systems are over-approximated by GSPDIs subject to two measures of precision. We prove soundness, completeness, and termination of both algorithms, and discuss their implementation.
A Computatuional Analysis of the Reachability Problem for a Class of Hybrid Dynamical Systems
1996
Hybrid systems possess continuous dynamics de ned within regions of state spaces and discrete transitions among the regions. Many practical control veri cation and synthesis tasks can be reduced to reachability problems for these systems that decide if a particular state-space region is reachable from an initial operating region. In this paper, we present a computational analysis of the face reachability problem for a class of three-dimensional dynamical systems whose state spaces are de ned by piecewise constant vector elds and whose trajectories never return to a state-space region once they exit the region. These systems represent a restricted class of control systems whose dynamics results from a juxtaposition of piecewise parameterized vector elds. We had previously developed a computational algorithm for synthesizing the desired dynamics of a system in phase space by piecing together vector elds geometrically. We demonstrate in this paper that the reachability problem for this class of systems is decidable while the computation is provably intractable (i.e., PSPACE-hard). We prove the intractability via a reduction of satis ability of quanti ed boolean formulas to this reachability problem. This result sheds light on the computational complexity of phase-space based control synthesis methods and extends the work of Asarin, Maler, and Pnueli 2] that proves computational undecidability for three-dimensional constant-derivative systems.
2013 Conference on Control and Fault-Tolerant Systems (SysTol), 2013
Ahstract-This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The al gorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerody namic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.
A Computational Analysis of the Reachability Problem for a Class of Hybrid Dynamical Systems
1997
Hybrid systems possess continuous dynamics defined within regions of state spaces and discrete transitions among the regions. Many practical control verification and synthesis tasks can be reduced to reach ability problems for these systems that decide if a particular state-space region is reachable from an initial operating region. In this paper, we present a computational analysis of the face reachability problem for a class of three-dimensional dynamical systems whose state spaces are defined by piecewise constant vector fields and whose trajectories never return to a state-space region once they exit the region. These systems represent a restricted class of control systems whose dynamics results from a juxtaposition of piecewise parameterized vector fields. We had previously developed a computational algorithm for synthesizing the desired dynamics of a system in phase space by piecing together vector fields geometrically. We demonstrate in this paper that the reachability problem for this class of systems is decidable while the computation is provably intractable (i.e., PSPACE-hard). We prove the intractability via a reduction of satisfiability of quantified boolean formulas to this reachability problem. This result sheds light on the computational complexity of phase-space based control synthesis methods and extends the work of Asarin, Maler, and Pnueli [2] that proves computational undecidability for three-dimensional constant-derivative systems.