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35
Controllers for Reachability Specifications for Hybrid Systems
 Automatica
, 1999
"... The problem of systematically synthesizing hybrid controllers which satisfy multiple control objectives is considered. We present a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisfies the most important objective (which we ..."
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Cited by 132 (40 self)
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The problem of systematically synthesizing hybrid controllers which satisfy multiple control objectives is considered. We present a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisfies the most important objective (which we refer to as safety). The system performance with respect to lower priority objectives (which we refer to as efficiency) can then be optimized within this class. We motivate our approach by showing how the proposed synthesis technique simplifies to well known results from supervisory control and pursuit evasion games when restricted to purely discrete and purely continuous systems respectively. We then illustrate the application of this technique to two examples, one hybrid (the steam boiler benchmark problem), and one primarily continuous (a flight vehicle management system with discrete flight modes). 1 Introduction Hybrid systems, or systems that involve the interaction of discrete and co...
A New Computational Approach to RealTime Trajectory Generation for Constrained Mechanical Systems
, 2000
"... Preliminary results of a new computational approach to generate aggressive trajectories in realtime for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that rea ..."
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Cited by 84 (20 self)
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Preliminary results of a new computational approach to generate aggressive trajectories in realtime for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that realtime trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the NTG software package. Keywords: Realtime optimization, nonlinear control design, optimal control, constrained trajectory generation, guidance. 1
Receding Horizon Control of Nonlinear Systems: A Control . . .
, 2000
"... n Automatic Control, pages 898 907, 1990. J. Shamma and M. Athans. Guaranteed properties of gain scheduled control for linear parametervarying plants. Automatica, pages 559 564, 1991. J. Shamma and M. Athans. Gainscheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, ..."
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Cited by 46 (4 self)
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n Automatic Control, pages 898 907, 1990. J. Shamma and M. Athans. Guaranteed properties of gain scheduled control for linear parametervarying plants. Automatica, pages 559 564, 1991. J. Shamma and M. Athans. Gainscheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, 12(3):101 107, June 1992. [Sch96] A. Schwartz. Theory and Implementation of Numerical Methods Based on RungeKutta Integration for Optimal Control Problems. PhD Disser tation, University of California, Berkeley, 1996. [SCH+00] M. Sznaier, J. Cloutier, R. Hull, D. Jacques, and C. Mracek. Reced ing horizon control lyapunov function approach to suboptimal regula tion of nonlinear systems. Journal of Guidance, Control, and Dynamics, 23(3):399 405, 2000. [SD90] M. Sznaier and M. J. Damborg. Heuristically enhanced feedback con trol of constrained discretetime linear systems. Automatica, 26:521 532, 1990. [SMR99] P. Scokaert, D. Mayne, and J. Rawlings. Suboptimal model predictive cont
Unconstrained Receding Horizon Control with No Terminal Cost
, 2001
"... In this paper, we discuss a stabilizing receding horizon scheme for unconstrained nonlinear systems. Using Dini's theorem on the uniform convergence of functions, we show that there always exist a finite horizon length for which the corresponding receding horizon scheme is stabilizing without u ..."
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Cited by 42 (10 self)
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In this paper, we discuss a stabilizing receding horizon scheme for unconstrained nonlinear systems. Using Dini's theorem on the uniform convergence of functions, we show that there always exist a finite horizon length for which the corresponding receding horizon scheme is stabilizing without using terminal costs and/or constraints.
Unconstrained RecedingHorizon Control of Nonlinear Systems
 IEEE Trans. Auto. Contr
, 2001
"... It is well known that unconstrained infinitehorizon optimal control may be used to construct a stabilizing controller for a nonlinear system. In this note, we show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate t ..."
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Cited by 21 (4 self)
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It is well known that unconstrained infinitehorizon optimal control may be used to construct a stabilizing controller for a nonlinear system. In this note, we show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon costtogo using, as terminal cost, an appropriate control Lyapunov function. Roughly speaking, the terminal control Lyapunov function (CLF) should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby relaxing the requirement that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). Moreover, it is easily seen that both CLF and infinitehorizon optimal control approaches are limiting cases of our receding horizon strategy.
Computing controllers for nonlinear hybrid systems
 in Lecture Notes in Computer Science, Hybrid Systems: Computation and Control
, 1999
"... Abstract. We discuss a procedure for synthesizing controllers for safety specifications for hybrid systems. The procedure depends on the construction of the set of states of a continuous dynamical system that can be driven to a subset of the state space, avoiding another subset of the state space (t ..."
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Cited by 14 (6 self)
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Abstract. We discuss a procedure for synthesizing controllers for safety specifications for hybrid systems. The procedure depends on the construction of the set of states of a continuous dynamical system that can be driven to a subset of the state space, avoiding another subset of the state space (the ReachAvoid set). We present a new characterization of the ReachAvoid set in terms of the solution of a pair of coupled HamiltonJacobi partial differential equations. We also discuss a computational algorithm for solving such partial differential equations and demonstrate its effectiveness on numerical examples. 1
Multiobjective hybrid controller synthesis
 Proceedings of International Workshop HART97, number 1201 in Lecture Notes in Computer Science
, 1997
"... We present a methodcllogy for synthesizing hybrid controllers that meet multiple control objectives. Our methodology uses game theoretic techniques to classify all controls that can be used to meet the high priority objectives. Lower priority objectives are then optimized within this class. 1 l[ntro ..."
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Cited by 14 (7 self)
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We present a methodcllogy for synthesizing hybrid controllers that meet multiple control objectives. Our methodology uses game theoretic techniques to classify all controls that can be used to meet the high priority objectives. Lower priority objectives are then optimized within this class. 1 l[ntroduction Hybrid systems, that is systems that involve the interaction of discrete and continuous dynamics, have recently attracted considerable attention (for a discussion of research directions in this field see [l]). In this paper we address hybrid control problems, in particular ones where multiple requirements are imposed on the design. In such st multiobjective setting some of the requirements are usually assumed to be more important than others, either explicitly or implicitly. For simplicity we restrict lour attention to two performance criteria. We will use ~afety to refer to the high priority criterion and eficienc y to refer to the low priority one. Using optimal control tools we attempt to determine the largest controlled invariant safe set, i.e. the largest set of states for which there exists a control such that the safety objective ciln be met. In the process we also determine the class of least restrictive safe controls, i.e. all the controls that can be used to meet the safety objective from the safe states. The efficiency objective can then be optimized within this class. The resulting controller will typically be hybrid as it involves switching between the safe and efficient controllers. Our analysis is based on the hybrid system modeling formalism introduced in [2]. The design algorithm (Section 2) is motivated by three examples. The first is ‘Research supported by the ARO under grant DAAH 0495
VIATO  Visual Interactive Aircraft Trajectory Optimization
 IEEE Transaction on Systems, Man, and Cybernetics, Part C: Applications and Reviews
, 1999
"... An approach toward the automated solution of aircraft trajectory optimization problems is introduced and implemented in an interactive program called visual interactive aircraft trajectory optimization (VIATO). This MS Windowscompatible software produces minimum time trajectories to a fixed or movin ..."
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Cited by 10 (6 self)
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An approach toward the automated solution of aircraft trajectory optimization problems is introduced and implemented in an interactive program called visual interactive aircraft trajectory optimization (VIATO). This MS Windowscompatible software produces minimum time trajectories to a fixed or moving target. It is easy to use by nonexperts as no previous knowledge of the methods of optimal control theory or mathematical modeling are needed. VIATO consists of a graphical user interface, an optimization server, and a model server. In VIATO, different aircraft types are represented by a set of parameters. The equations of motion and state as well as control constraints are fixed in advance. Since the objective function is also specified, the user avoids the modeling and explicit formulation of optimal control problems. Reliable convergence to an approximate optimal solution is achieved by converting the original optimal control problem into a finite dimensional optimization problem. The parameterized problem is solved using nonlinear programming.
Singular arcs in the generalized Goddard’s Problem
, 2007
"... We investigate variants of Goddard’s problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this article, performing an analysis based on the Pontryagin Maximum Principle, we prove that optimal traj ..."
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Cited by 9 (6 self)
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We investigate variants of Goddard’s problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this article, performing an analysis based on the Pontryagin Maximum Principle, we prove that optimal trajectories may involve singular arcs (along which the norm of the thrust is neither zero nor maximal), that are computed and characterized. Numerical simulations are carried out, both with direct and indirect methods, demonstrating the relevance of taking into account singular arcs in the control strategy. The indirect method we use is based on our previous theoretical analysis and consists in combining a shooting method with an homotopic method. The homotopic approach leads to a quadratic regularization of the problem and is a way to tackle with the problem of nonsmoothness of the optimal control.