Marina Hebe Murillo

Distributed Model Predictive Control Based on Dynamic Games

Model predictive control (MPC) is widely recognized as a high performance, yet practical, control technology. This model-based control strategy solves at each sample a discrete-time optimal control problem over a finite horizon, producing a control input sequence. An attractive attribute of MPC technology is its ability to systematically account for system constraints. The theory of MPC for linear systems is well developed; all aspects such as stability, robustness,feasibility and optimality have been extensively discussed in the literature (see, e.g., (Bemporad & Morari, 1999; Kouvaritakis & Cannon, 2001; Maciejowski, 2002; Mayne et al., 2000)). The effectiveness of MPC depends on model accuracy and the availability of fast computational resources. These requirements limit the application base for MPC. Even though, applications abound in process industries (Camacho & Bordons, 2004), manufacturing (Braun et al., 2003), supply chains (Perea-Lopez et al., 2003), among others, are becoming more widespread. Two common paradigms for solving system-wide MPC calculations are centralised and decentralised strategies. Centralised strategies may arise from the desire to operate the system in an optimal fashion, whereas decentralised MPC control structures can result from the incremental roll-out of the system development. An effective centralised MPC can be difficult, if not impossible to implement in large-scale systems (Kumar & Daoutidis, 2002; Lu, 2003). In decentralised strategies, the system-wide MPC problem is decomposed into subproblems by taking advantage of the system structure, and then, these subproblems are solved independently. In general, decentralised schemes approximate the interactions between subsystems and treat inputs in other subsystems as external disturbances. This assumption leads to a poor systemperformance (Sandell Jr et al., 1978; Siljak, 1996). Therefore, there is a need for a cross-functional integration between the decentralised controllers, in which a coordination level performs steady-state target calculation for decentralised controller (Aguilera & Marchetti, 1998; Aske et al., 2008; Cheng et al., 2007; 2008; Zhu & Henson, 2002). Several distributed MPC formulations are available in the literature. A distributed MPC framework was proposed by Dumbar and Murray (Dunbar & Murray, 2006) for the class 4

Iterated non-linear model predictive control based on tubes and contractive constraints.

This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle.

A Real-Time Path-Planning Algorithm based on Receding Horizon Techniques

In this article we present a real-time path-planning algorithm that can be used to generate optimal and feasible paths for any kind of unmanned vehicle (UV). The proposed algorithm is based on the use of a simplified particle vehicle (PV) model, which includes the basic dynamics and constraints of the UV, and an iterated non-linear model predictive control (NMPC) technique that computes the optimal velocity vector (magnitude and orientation angles) that allows the PV to move toward desired targets. The computed paths are guaranteed to be feasible for any UV because: i) the PV is configured with similar characteristics (dynamics and physical constraints) as the UV, and ii) the feasibility of the optimization problem is guaranteed by the use of the iterated NMPC algorithm. As demonstration of the capabilities of the proposed path-planning algorithm, we explore several simulation examples in different scenarios. We consider the existence of static and dynamic obstacles and a follower condition.

Adaptive arrival cost update for improving Moving Horizon Estimation performance

Moving horizon estimation is an efficient technique to estimate states and parameters of constrained dynamical systems. It relies on the solution of a finite horizon optimization problem to compute the estimates, providing a natural framework to handle bounds and constraints on estimates, noises and parameters. However, the approximation of the arrival cost and its updating mechanism are an active research topic. The arrival cost is very important because it provides a mean to incorporate information from previous measurements to the current estimates and it is difficult to estimate its true value. In this work, we exploit the features of adaptive estimation methods to update the parameters of the arrival cost. We show that, having a better approximation of the arrival cost, the size of the optimization problem can be significantly reduced guaranteeing the stability and convergence of the estimates. These properties are illustrated through simulation studies.