A Semismooth Predictor Corrector Method for Suboptimal Model Predictive Control

Abstract

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. D. Liao-McPherson and I.V. Kolmanovsky are with the University of Michigan, Ann Arbor. Email:{dliaomcp,ilya}@umich.edu. M. M. Nicotra is with the University of Colorado Boulder.

A Chance Constraint Predictive Control and Estimation Framework for Spacecraft Descent with Field Of View Constraints

“…Both trajectories consist of a constant descent rate phase and hover at a point phase. At each time step the linearizations (8)(9)(10) The simulation parameters are given below. The place command in MATLAB was used to compute K t .…”

“…The translational component of the model is taken from [8], and rotational component based on an example in [9]. ξ is the state vector.…”

“…Successive convexification approaches such as those in [11] can admit solutions to opimality of a non-convex optimal control (OCP) problem. Such a non-convex OCP can be constructed with f propogated dynamics as opposed to (8)(9), however these types of algorithms take many iterations and Jacobian evaluations per time instant. Instead of the approach of solving the non-convex OCP, the constraints introduced aim to confine the system (11-12) such that the LQMPC law is acting on a suitably convex region of the system.…”

Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

“…The latter property is important since it is a sufficient condition for Lipschitz continuity of the optimal value function and thus for robust stability. This paper builds upon the results in [33] which analyzes the stability of MPC implemented using a suboptimal semismooth predictor-corrector (SSPC) method. Specifically, we generalize the previous results for suboptimal SSPC to a wide class of optimizers which are at least q-linearly convergent.…”