The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs
SIAM Journal on Optimization
Survey paper: Research on probabilistic methods for control system design
Automatica (Journal of IFAC)
SIAM Journal on Optimization
Quasi-Min-Max MPC algorithms for LPV systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Convexity and convex approximations of discrete-time stochastic control problems with constraints
Automatica (Journal of IFAC)
Lyapunov-based model predictive control of stochastic nonlinear systems
Automatica (Journal of IFAC)
Randomized Algorithms for Analysis and Control of Uncertain Systems: With Applications
Randomized Algorithms for Analysis and Control of Uncertain Systems: With Applications
Hi-index | 22.14 |
A stochastic receding-horizon control approach for constrained Linear Parameter Varying discrete-time systems is proposed in this paper. It is assumed that the time-varying parameters have stochastic nature and that the system's matrices are bounded but otherwise arbitrary nonlinear functions of these parameters. No specific assumption on the statistics of the parameters is required. By using a randomization approach, a scenario-based finite-horizon optimal control problem is formulated, where only a finite number M of sampled predicted parameter trajectories ('scenarios') are considered. This problem is convex and its solution is a priori guaranteed to be probabilistically robust, up to a user-defined probability level p. The p level is linked to M by an analytic relationship, which establishes a tradeoff between computational complexity and robustness of the solution. Then, a receding horizon strategy is presented, involving the iterated solution of a scenario-based finite-horizon control problem at each time step. Our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time, either deterministically, or with probability no smaller than p. The features of the approach are illustrated by a numerical example.