Dominic Liao-McPherson

Marco M. Nicotra, Dominic Liao-McPherson, Ilya V. Kolmanovsky

This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal control problem can be embedded into the internal states of a dynamic control law which runs in parallel to the system. Using input to state stability arguments, it is shown that if the controller dynamics are sufficiently fast with respect to the plant dynamics, the interconnection between the two systems is asymptotically stable. Additionally, it is shown that, by augmenting the proposed scheme with an add-on unit known as an Explicit Reference Governor, it is possible to drastically increase the set of initial conditions that can be steered to the desired reference without violating the constraints. Numerical examples demonstrate the effectiveness of the proposed scheme.

Dominic Liao-McPherson, Marco Nicotra, Ilya Kolmanovsky

Real-time optimization problems are ubiquitous in control and estimation, and are typically parameterized by incoming measurement data and/or operator commands. This paper proposes solving parameterized constrained nonlinear programs using a semismooth predictor-corrector (SSPC) method. Nonlinear complementarity functions are used to reformulate the first order necessary conditions of the optimization problem into a parameterized non-smooth root-finding problem. Starting from an approximate solution, a semismooth Euler-Newton algorithm is proposed for tracking the trajectory of the primal-dual solution as the parameter varies over time. Active set changes are naturally handled by the SSPC method, which only requires the solution of linear systems of equations. The paper establishes conditions under which the solution trajectories of the root-finding problem are well behaved and provides sufficient conditions for ensuring boundedness of the tracking error. Numerical case studies featuring the application of the SSPC method to nonlinear model predictive control are reported and demonstrate the advantages of the proposed method.

Simon J. Jones, Dominic Liao-McPherson, Marco M. Nicotra

This paper details a novel indirect method for solving constrained optimal control problems (OCPs) directly in continuous-time function space. The KKT conditions are embedded in a non-smooth complementarity function, which enables their reformulation as a rootfinding problem in Banach space. This problem is then solved using a non-smooth Newton method. Finally, the paper shows that the Newton update can be obtained by solving a modified differential Riccati equation, where the cost terms are reweighted at every iteration based on the constraint multipliers. Numerical simulations show the effectiveness of the method, which converges superlinearly up to the tolerance of the ODE solver.

Dominic Liao-McPherson, Marco Nicotra, Ilya Kolmanovsky

Suboptimal model predictive control is a technique that can reduce the computational cost of model predictive control (MPC) by exploiting its robustness to incomplete optimization. Instead of solving the optimal control problem exactly, this method maintains an estimate of the optimal solution and updates it at each sampling instance. The resulting controller can be viewed as a dynamic compensator which runs in parallel with the plant. This paper explores the use of the semismooth predictor-corrector method to implement suboptimal MPC. The dynamic interconnection of the combined plant-optimizer system is studied using the input-to-state stability framework and sufficient conditions for closed-loop asymptotic stability and constraint enforcement are derived using small gain arguments. Numerical simulations demonstrate the efficacy of the scheme.