Control of Uncertain Hybrid Nonlinear Systems Using Particle Filters

This paper proposes an optimization-based algorithm for the control of uncertain hybrid nonlinear systems. The considered system class combines the nondeterministic evolution of a discrete-time Markov process with the deterministic switching of continuous dynamics which itself contains uncertain elements. A weighted particle filter approach is used to approximate the uncertain evolution of the system by a set of deterministic runs. The desired control performance for a finite time horizon is encoded by a suitable cost function and a chance-constraint, which restricts the maximum probability for entering unsafe state sets. The optimization considers input and state constraints in addition. It is demonstrated that the resulting optimization problem can be solved by techniques of conventional mixed-integer nonlinear programming (MINLP). As an illustrative example, a path planning scenario of a ground vehicle with switching nonlinear dynamics is presented.