The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Linear robust control
A Smooth Converse Lyapunov Theorem for Robust Stability
SIAM Journal on Control and Optimization
Optimal Sampled-Data Control Systems
Optimal Sampled-Data Control Systems
Information Processing Letters
Region stability proofs for hybrid systems
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
Automatic verification of control system implementations
EMSOFT '10 Proceedings of the tenth ACM international conference on Embedded software
Abstraction Refinement for Stability
ICCPS '11 Proceedings of the 2011 IEEE/ACM Second International Conference on Cyber-Physical Systems
Model checking of hybrid systems: from reachability towards stability
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Accuracy-Guaranteed Bit-Width Optimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Improved Interval-Based Characterization of Fixed-Point LTI Systems With Feedback Loops
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Supervisor synthesis for controller upgrades
Proceedings of the Conference on Design, Automation and Test in Europe
Synthesis of fixed-point programs
Proceedings of the Eleventh ACM International Conference on Embedded Software
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Software implementations of controllers for physical systems are at the core of many embedded systems. The design of controllers uses the theory of dynamical systems to construct a mathematical control law that ensures that the controlled system has certain properties, such as asymptotic convergence to an equilibrium point, and optimizes some performance criteria such as LQR-LQG. However, owing to quantization errors arising from the use of fixed-point arithmetic, the implementation of this control law can only guarantee practical stability: under the actions of the implementation, the trajectories of the controlled system converge to a bounded set around the equilibrium point, and the size of the bounded set is proportional to the error in the implementation. The problem of verifying whether a controller implementation achieves practical stability for a given bounded set has been studied before. In this paper, we change the emphasis from verification to automatic synthesis. We give a technique to synthesize embedded control software that is Pareto optimal w.r.t. both performance criteria and practical stability regions. Our technique uses static analysis to estimate quantization-related errors for specific controller implementations, and performs stochastic local search over the space of possible controllers using particle swarm optimization. The effectiveness of our technique is illustrated using several standard control system examples: in most examples, we find controllers with close-to-optimal LQR-LQG performance but with implementation errors, hence regions of practical stability, several times as small.