(473c) Resource-Aware Model Predictive Control Using Adaptive Sampling

Model predictive control (MPC) has a long history in process control research as one of the few methods suited for handling constraints in an optimal control setting. In a typical MPC implementation, state measurements are received at the sampling time and the control action is obtained by solving, on-line, a model-based finite-horizon optimal control problem subject to state, control and stability constraints. Only the first part of the computed control trajectory is implemented until the next sampling time at which new state measurements are received to update the model state and re-solve the optimization problem. While many different MPC formulations currently exist in the literature, the MPC problem is often formulated and addressed within the classical feedback control paradigm in which the process output is passed at a fixed sampling rate to the controller which then generates the control input and in turn passes it back to the process.

The success of this paradigm notwithstanding, recent years have witnessed a number of calls for re-examining the conventional feedback control paradigm and expanding it in ways that account for the increasing complexity of the process/controller interface which features additional information-processing steps that need be accounted for. For example, with the emergence of applications involving wireless sensor and actuator networks, constraints on the information collection, processing and transmission capabilities of the measurement system and the communication medium are becoming commonplace and require attention in the MPC system design. In some of these applications, it is advantageous, if not necessary, to collect and transfer measurements at a variable (rather than a fixed) rate in order to optimize performance under limited resources.

In this contribution we present a framework for the design of resource-aware model predictive controllers for constrained nonlinear systems subject to sensor-controller communication constraints. The main objective is to enforce the desired closed-loop stability and optimality properties with minimal measurement sampling and/or sensor-controller communication. To this end, we initially design a Lyapunov-based model predictive controller that enforces closed-loop stability within a well-characterized stability region for a given sampling/communication rate. The controller minimizes an appropriate cost functional defined over the prediction horizon subject to state and control constraints, and includes a stability constraint that ensures the decay of the Lyapunov function during the sampling interval. The closed-loop stability properties are characterized in terms of a state-dependent bound on the decay of the Lyapunov function that can be tuned by proper selection of the sampling period and the controller design parameters. This characterization is then used to devise a dynamic sampling/communication policy that adaptively adjusts the rate of information transfer from the sensors to the controller based on the evolution of the Lyapunov function within the stability region. The idea is to reduce the sampling/communication rate (or suspend communication altogether) for times when the prescribed stability bound is satisfied. During such periods, the control action computed from the model-based optimization is implemented without any model updates. At times when the state begins to breach the prescribed stability bound, the sampling/communication rate is increased (or communication is fully restored) to allow more frequent model updates. Switched system techniques are used to analyze closed-loop stability and derive precise conditions for the implementation of the proposed adaptive sampling policy. Finally, the theoretical results are illustrated using a chemical process example.