Computationally Aware Control of Cyber-Physical Systems: A Hybrid Model Predictive Control Approach

Abstract

Cyber-Physical Systems (CPS) are systems of collaborating computational elements controlling physical entities via communication. Such systems involve control processes of physical entities and computational processes. The control complexities originated from the physical dynamics and systematic constraints are difficult for traditional control approaches (e.g., PID control) to handle without an exponential increase in design/test etc. costs. Model predictive control (MPC) predicts and produces optimized control inputs based on its predictive model according to a cost function under given constraints. This control scheme has some attractive features for CPSs: it handles constraints systematically, and generates behavior prediction with respective control inputs simultaneously. However, MPC approaches are computationally intensive, and the computation burden generally grows as a predictive model more closely approximates a nonlinear plant (in order to achieve more accurate behavior). The computational burden of predictive methods can be addressed through model reduction at the cost of higher divergence between prediction and actual behavior. This work introduces a metric called uncontrollable divergence, and proposes a mechanism using the metric to select the model to use in the predictive controller (assuming that a set of predictive models are available). The metric reveals the divergence between predicted and true states caused by return time and model mismatch. More precisely, a map of uncontrollable divergence plotted over the state space gives the criterion to judge where a specific model can outperform others. With this metric and the mechanism, this work designs a controller that switches at runtime among a set of predictive controllers in which respective models are deployed. The resulting controller is a hybrid predictive controller. In addition to design and runtime tools, this work also studies stability conditions for hybrid model predictive controllers in two approaches. One is average dwell time based, and it does not rely on the offline computation that studies the system properties. The other one uses a reference Lyapunov function instead of multiple Lyapunov functions derived from multiple predictive controllers. This approach implicitly depends on the offline numerical solutions of certain systematic properties. The term "boundedness" is preferable in this context since it accepts numerical error and approximations. Two examples, vertical takeoff and landing aerial vehicle control and ground vehicle control, are used to demonstrate the approach of hybrid MPC.