Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Maximum Principle for a Hybrid System Via Singular Perturbations
SIAM Journal on Control and Optimization
Multiple Agent Hybrid Control Architecture
Hybrid Systems
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Computing Controllers for Nonlinear Hybrid Systems
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Control Synthesis for a Class of Hybrid Systems Subject to Configuration-Based Safety Constraints
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
Controllers for reachability specifications for hybrid systems
Automatica (Journal of IFAC)
Specification-guided controller synthesis for linear systems and safe linear-time temporal logic
Proceedings of the 16th international conference on Hybrid systems: computation and control
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An algorithm for computing the maximal controlled invariant set and the least restrictive controller for discrete time systems is proposed. We show how the algorithm can be encoded using quantifier elimination, which leads to a semi-decidability result for definable systems. For discrete time linear systems with all sets specified by linear inequalities, a more efficient implementation is proposed using linear programming and Fourier elimination. If in addition the system is in controllable canonical form, the input is scalar and unbounded, the disturbance is scalar and bounded and the initial set is a rectangle, then the problem is decidable.