The control of dynamic systems, which aims to minimize the deviation of state variables from reference values in a continuous state space, is a central domain of cybernetics and control theory. The objective of action planning is to find feasible state trajectories in a discrete state space from an initial state to a state satisfying the goal conditions, which in principle addresses the same issue on a more abstract level. We combine these approaches to switch between dynamic system characteristics on the fly, and to generate control input sequences that affect both discrete and continuous state variables. Our approach (called Domain Predictive Control) is applicable to hybrid systems with linear dynamics and discretizable inputs.
Planning-based methods to guide switched hybrid systems from an initial state into a desired goal region opens an interesting field for control. The idea of the Domain Predictive Control (DPC) approach is to generate input signals affecting both the numerical states and the modes of the system by stringing together atomic actions to a logically consistent plan. However, the existing DPC approach is restricted in the sense that a discrete and pre-defined input signal is required for each action. In this paper, we extend the approach to deal with symbolic states. This allows for the propagation of reachable regions of the state space emerging from actions with inputs that can be arbitrarily chosen within specified input bounds. This symbolic extension enables the applicability of DPC to systems with bounded inputs sets and increases its robustness due to the implicitly reduced search space. Moreover, precise numeric goal states instead of goal regions become reachable.
In planning, hybrid system states consisting of logical and numerical variables are usually assumed to be completely known. In particular, for numerical state variables full knowledge of their exact values is assumed. However, in real world applications states are results of noisy measurements and imperfect actuators. Therefore, a planned sequence of state transitions might fail to lead a hybrid system to the desired goal. We show how to propagate and reason about uncertain state information directly in the planning process, enabling hybrid systems to find plans that satisfy numerical goals with predefined confidence.
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