Lyapunov-based Model Predictive Control of Nonlinear Systems Subject to Time-Varying Measurement Delay

The problem of designing feedback control systems for nonlinear systems subject to time-varying measurement delays is a fundamental one and its solution can find significant application in a number of control engineering problems including, for example, design of networked control systems (NCS). The importance of time delays in the context of networked control systems has motivated significant research effort in modeling such delays and designing control systems to deal with them, primarily in the context of linear systems (e.g., [1, 2, 3, 4, 5, 6]). This work deals with the design of predictive controllers for nonlinear system subject to time-varying measurement delay in the feedback loop. The available results on Lyapunov-based MPC [7, 8, 9, 10] do not account for the effect of timevarying measurement delays, and when time-varying measurement delays are taken into account, these schemes are not guaranteed to maintain the desired closed-loop stability properties. We also note that most of the available results on MPC of systems with delays deal with linear systems (e.g., [11, 12]). In this work, we modify the Lyapunov-based MPC schemes developed previously by our group to take into account time-varying measurement delay, both in the optimization problem formulation and in the controller implementation. The proposed LMPC scheme allows for an explicit characterization of the stability region, guarantees practical stability in the absence of delay, and guarantees that the stability region is an invariant set for the closed-loop system if the maximum delay is shorter than a given constant that depends on the parameters of the system and the Lyapunov-based controller that is used to formulate the optimization problem.