# A game theoretic approach to controller design for hybrid systems

@article{Tomlin2000AGT, title={A game theoretic approach to controller design for hybrid systems}, author={Claire J. Tomlin and John Lygeros and S. Shankar Sastry}, journal={Proceedings of the IEEE}, year={2000}, volume={88}, pages={949-970} }

We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and… Expand

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#### References

SHOWING 1-10 OF 106 REFERENCES

A unified framework for hybrid control: model and optimal control theory

- Computer Science, Mathematics
- IEEE Trans. Autom. Control.
- 1998

This work introduces a mathematical model of hybrid systems as interacting collections of dynamical systems, evolving on continuous-variable state spaces and subject to continuous controls and discrete transitions, and develops a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework. Expand

Theory of hybrid systems and discrete event systems

- Mathematics
- 1996

A continuous system has a continuous state space and an evolution law given by a differential or a difference equation. A discrete event system is modeled by an automaton which changes state in… Expand

Decidable Controller Synthesis for Classes of Linear Systems

- Computer Science
- HSCC
- 2000

This paper shows that for classes of linear systems, the controller synthesis problem is decidable: There exists a computational algorithm which, after a finite number of steps, will exactly compute the least restrictive controller. Expand

An Optimal Control Theory for Discrete Event Systems

- Mathematics
- 1998

In certain discrete event applications it may be desirable to find a particular controller, within the set of acceptable controllers, which optimizes some quantitative performance measure. In this… Expand

Controllers for reachability specifications for hybrid systems

- Engineering, Computer Science
- Autom.
- 1999

This work presents a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisfies the most important objective and shows 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. Expand

H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach

- Computer Science
- IEEE Trans. Autom. Control.
- 1996

The authors believe that the H-infinity-optimal control theory is now at a stage where it can easily be incorporated into a second-level graduate course in a control curriculum, that would follow a basic course in linear control theory covering LQ and LQG designs. Expand

Level Set Methods for Computation in Hybrid Systems

- Computer Science
- HSCC
- 2000

This work presents an implementation of an exact reachability operator for nonlinear hybrid systems, and an equivalent formulation is developed of the key equations governing the continuous state reachability. Expand

On controller synthesis for nonlinear hybrid systems

- Engineering
- Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)
- 1998

We present a methodology for synthesizing controllers for hybrid systems to satisfy safety specifications. Motivated by an application to conflict resolution for aircraft, we present a conceptual… Expand

Control Synthesis for a Class of Hybrid Systems Subject to Configuration-Based Safety Constraints

- Engineering, Computer Science
- HART
- 1997

An algorithm is presented for the synthesis of minimally restrictive legal controllers for CHMs with rate-limited dynamics, where legal guards are conjunctions or disjunctions of atomic formulas in the dynamic variables. Expand

Hierarchical, Hybrid Control of Large Scale Systems

- Engineering
- 1996

This dissertation presents a hierarchical, hybrid point of view to the control of large-scale systems. The analysis is based on a new hybrid dynamical system formulation that allows for the modelling… Expand