EE291E Lecture Notes 10. Controller Synthesis for Hybrid Systems
نویسنده
چکیده
In the last several lectures, we have discussed controller synthesis for: • Discrete Systems: design is characterized by a fixed point of a difference equation • Continuous Systems: design is characterized by a fixed point of a partial differential equation In each case, the solution is characterized as a fixed point of an equation, which we refer to as the Hamilton-Jacobi equation. In these lecture notes, we bring the discrete and continuous parts together, and discuss the problem of designing controllers for hybrid systems. Our treatment follows that of [1, 2, 3, 4]. To avoid technical problems we assume that: 1. f is Lipschitz continuous in x and continuous in w ∈ In; 2. for all q ∈ Q and for all σ ∈ Σ, w ∈ W , Dom(q) is an open set. Part 1 is standard, and is needed for existence of continuous evolution. Part 2 implies that we need not worry about what happens on the boundary of the invariant set. Finally, part 3 (together with part 2) implies that the controller cannot block the system execution. Notice that this assumption is not symmetric for (σ 1 , u) and (σ 2 , d). The reason is that, since we 1
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