Results 1 - 10
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30
Linear time logic control of discrete-time linear systems
- IEEE Transactions on Automatic Control
, 2006
"... Abstract. The control of complex systems poses new challenges that fall beyond the traditional methods of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several interacting submodules within a system. The desired objectives are no ..."
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Cited by 61 (4 self)
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Abstract. The control of complex systems poses new challenges that fall beyond the traditional methods of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several interacting submodules within a system. The desired objectives are no longer captured by usual control specifications such as stabilization or output regulation. Instead, we consider specifications given by Linear Temporal Logic (LTL) formulas. We show that existence of controllers for discrete-time controllable linear systems and LTL specifications can be decided and that such controllers can be effectively computed. The closed-loop system is of hybrid nature, combining the original continuous dynamics with the automatically synthesized switching logic required to enforce the specification. 1.
A control problem for affine dynamical systems on a full-dimensional polytope
- AUTOMATICA
, 2004
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Reachability and control synthesis for piecewise-affine hybrid systems on simplices
- IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2006
"... In this paper, we consider the synthesis of control laws for piecewise-affine hybrid systems on simplices. The construction is based on the solution to the control-to-facet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit alg ..."
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Cited by 47 (1 self)
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In this paper, we consider the synthesis of control laws for piecewise-affine hybrid systems on simplices. The construction is based on the solution to the control-to-facet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit algorithm using only linear algebra and reach-set computations for automata; no numerical integration is required. The method is conservative, in that it may fail to find a control law where one exists, but one cannot hope for a sharp algorithm for control synthesis since reachability for piecewise-affine hybrid systems is undecidable.
Control of multi-affine systems on rectangles with applications to hybrid biomolecular networks
- In: Proc. CDC’02. (2002
, 2002
"... Given a multi-affine system on an Æ-dimensional rectangle, the problem of reaching a particular facet, using multiaffine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the v ..."
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Cited by 35 (10 self)
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Given a multi-affine system on an Æ-dimensional rectangle, the problem of reaching a particular facet, using multiaffine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the rectangle, and a method for constructing a multi-affine state feedback solution is presented. The technique is applied to the control of hybrid models of bioregulatory networks. 1
Model checking LTL over controllable linear systems is decidable
- of Lecture Notes in Computer Science
, 2003
"... Abstract. The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesi ..."
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Cited by 31 (2 self)
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Abstract. The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesis by showing decidability of model checking Linear Temporal Logic (LTL) formulas over discrete time, controllable, linear systems. This result follows from the construction of a language equivalent, finite abstraction of a control system based on a set of finite observations which correspond to the atomic propositions appearing in a given LTL formula. Furthermore, the size of this abstraction is shown to be polynomial in the dimension of the control system and the number of observations. These results open the doors for verification and synthesis of continuous and hybrid control systems from LTL specifications. 1
From discrete specifications to hybrid control,” Decision and Control
- Proc. 42nd IEEE Conference
, 2003
"... endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution m ..."
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Cited by 15 (2 self)
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endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
Simple and Efficient Algorithms for Computing Smooth, Collision-Free Feedback Laws Over Given Cell Decompositions
"... This paper presents a novel approach to computing feedback laws in the presence of obstacles. Instead of computing a trajectory between a pair of initial and goal states, our algorithms compute a vector field over the entire state space; all trajectories obtained from following this vector field are ..."
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Cited by 13 (1 self)
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This paper presents a novel approach to computing feedback laws in the presence of obstacles. Instead of computing a trajectory between a pair of initial and goal states, our algorithms compute a vector field over the entire state space; all trajectories obtained from following this vector field are guaranteed to asymptotically reach the goal state. As a result, the vector field globally solves the navigation problem and provides robustness to disturbances in sensing and control. The vector field’s integral curves (system trajectories) are guaranteed to avoid obstacles and are C ∞ smooth. We construct a vector field with these properties by partitioning the space into simple cells, defining local vector fields for each cell, and smoothly interpolating between them to obtain a global vector field. We present an algorithm that computes these feedback controls for a kinematic point robot in an arbitrary dimensional space with piecewise linear boundary; the algorithm requires minimal preprocessing of the environment and is extremely fast during execution. For many practical applications in two-dimensional environments, full computation can be done in milliseconds. We also present an algorithm for computing feedback laws over cylindrical algebraic decompositions, thereby solving a smooth feedback version of the generalized piano movers’ problem.
Necessary and sufficient conditions for reachability on a simplex
- Automatica
, 1913
"... Abstract — The reachability problem has received significant attention in the hybrid control literature with many questions still left unanswered. In this paper we solve the general problem of reaching a set of facets of an n-dimensional simplex in finite time, for a system evolving with linear affi ..."
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Cited by 12 (1 self)
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Abstract — The reachability problem has received significant attention in the hybrid control literature with many questions still left unanswered. In this paper we solve the general problem of reaching a set of facets of an n-dimensional simplex in finite time, for a system evolving with linear affine dynamics. Necessary and sufficient conditions are presented in the form of inequalities on the vertices of the simplex, and a linear affine controller is constructed that solves the reachability problem. I.
Synthesis using approximately bisimilar abstractions: state-feedback controllers for safety specifications
- in Proceedings of 13th International Conference on Hybrid Systems: Computation and Control
, 2010
"... Abstract-In this paper, we present a hierarchical approach to time-optimal control using approximately bisimilar abstractions. Given a time-optimal controller for an abstraction, we present a specific procedure that allows us to compute a suboptimal controller for the original system. While the usu ..."
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Cited by 12 (2 self)
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Abstract-In this paper, we present a hierarchical approach to time-optimal control using approximately bisimilar abstractions. Given a time-optimal controller for an abstraction, we present a specific procedure that allows us to compute a suboptimal controller for the original system. While the usual controller refinement procedure produces dynamic controllers that may have limitations in terms of implementation cost and robustness, the static controllers we synthesize do not suffer from these issues. Moreover, we provide guarantees by bounding below and above the performances of the synthesized controller between performances of two time-optimal controllers for problems that can be made arbitrarily close by choosing sufficiently precise abstractions. Finally, we show the effectiveness of our approach by solving time-optimal control problems for switched systems.
Finite Bisimulations of Controllable Linear Systems
- Theoretical Computer Science
"... Finite abstractions of infinite state models have been critical in enabling and applying formal and algorithmic verification methods to continuous and hybrid systems. This has triggered the study and characterization of classes of continuous dynamics which can be abstracted by finite transition syst ..."
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Cited by 9 (2 self)
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Finite abstractions of infinite state models have been critical in enabling and applying formal and algorithmic verification methods to continuous and hybrid systems. This has triggered the study and characterization of classes of continuous dynamics which can be abstracted by finite transition systems. In this paper, we focus on synthesis rather than analysis. In this spirit, we show that given any discrete-time, linear control system satisfying a generic controllability property, and any finite set of observations restricted to the boolean algebra of Brunovsky sets, a finite bisimulation always exists and can be e#ectively computed.
