Adaptive Horizon Model Predictive Control and Al'brekht's Method

A standard way of finding a feedback law that stabilizes a control system to an operating point is to recast the problem as an infinite horizon optimal control problem. If the optimal cost and the optmal feedback can be found on a large domain around the operating point then a Lyapunov argument can be used to verify the asymptotic stability of the closed loop dynamics. The problem with this approach is that is usually very difficult to find the optimal cost and the optmal feedback on a large domain for nonlinear problems with or without constraints. Hence the increasing interest in Model Predictive Control (MPC). In standard MPC a finite horizon optimal control problem is solved in real time but just at the current state, the first control action is implimented, the system evolves one time step and the process is repeated. A terminal cost and terminal feedback found by Al'brekht's methoddefined in a neighborhood of the operating point is used to shorten the horizon and thereby make the nonlinear programs easier to solve because they have less decision variables. Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that MPC methods can be used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861

Direct data-driven control of constrained linear parameter-varying systems: A hierarchical approach

In many nonlinear control problems, the plant can be accurately described by a linear model whose operating point depends on some measurable variables, called scheduling signals. When such a linear parameter-varying (LPV) model of the open-loop plant needs to be derived from a set of data, several issues arise in terms of parameterization, estimation, and validation of the model before designing the controller. Moreover, the way modeling errors affect the closed-loop performance is still largely unknown in the LPV context. In this paper, a direct data-driven control method is proposed to design LPV controllers directly from data without deriving a model of the plant. The main idea of the approach is to use a hierarchical control architecture, where the inner controller is designed to match a simple and a-priori specified closed-loop behavior. Then, an outer model predictive controller is synthesized to handle input/output constraints and to enhance the performance of the inner loop. The effectiveness of the approach is illustrated by means of a simulation and an experimental example. Practical implementation issues are also discussed.Comment: Preliminary version of the paper "Direct data-driven control of constrained systems" published in the IEEE Transactions on Control Systems Technolog

Model Predictive Control for Spacecraft Rendezvous in Elliptical Orbits with On/Off Thrusters

IFAC Workshop on Advanced Control and Navigation for Autonomous Aerospace Vehicles. 08/06/2015. SevillaIn previous works, the authors have developed a trajectory planning algorithm for spacecraft rendezvous which computed optimal Pulse-Width Modulated (PWM) control signals, for circular and eccentric Keplerian orbits. The algorithm is initialized by solving the impulsive problem first and then, using explicit linearization and linear programming, the solution is refined until a (possibly local) optimal value is reached. However, trajectory planning cannot take into account orbital perturbations, disturbances or model errors. To overcome these issues, in this paper we develop a Model Predictive Control (MPC) algorithm based on the open-loop PWM planner and test it for elliptical target orbits with arbitrary eccentricity (using the linear time-varying Tschauner-Hempel model). The MPC is initialized by first solving the open-loop problem with the PWM trajectory planning algorithm. After that, at each time step, our MPC saves time recomputing the trajectory by applying the iterative linearization scheme of the trajectory planning algorithm to the solution obtained in the previous time step. The efficacy of the method is shown in a simulation study where it is compared to MPC computed used an impulsive-only approach

Stochastic model predictive control for constrained networked control systems with random time delay

In this paper the continuous time stochastic constrained optimal control problem is formulated for the class of networked control systems assuming that time delays follow a discrete-time, finite Markov chain . Polytopic overapproximations of the system's trajectories are employed to produce a polyhedral inner approximation of the non-convex constraint set resulting from imposing the constraints in continuous time. The problem is cast in a Markov jump linear systems (MJLS) framework and a stochastic MPC controller is calculated explicitly, oine, coupling dynamic programming with parametric piecewise quadratic (PWQ) optimization. The calculated control law leads to stochastic stability of the closed loop system, in the mean square sense and respects the state and input constraints in continuous time

Plug-and-Play Fault Detection and control-reconfiguration for a class of nonlinear large-scale constrained systems

This paper deals with a novel Plug-and-Play (PnP) architecture for the control and monitoring of Large-Scale Systems (LSSs). The proposed approach integrates a distributed Model Predictive Control (MPC) strategy with a distributed Fault Detection (FD) architecture and methodology in a PnP framework. The basic concept is to use the FD scheme as an autonomous decision support system: once a fault is detected, the faulty subsystem can be unplugged to avoid the propagation of the fault in the interconnected LSS. Analogously, once the issue has been solved, the disconnected subsystem can be re-plugged-in. PnP design of local controllers and detectors allow these operations to be performed safely, i.e. without spoiling stability and constraint satisfaction for the whole LSS. The PnP distributed MPC is derived for a class of nonlinear LSSs and an integrated PnP distributed FD architecture is proposed. Simulation results in two paradigmatic examples show the effectiveness and the potential of the general methodology

Robust moving horizon H∞ control of discrete time-delayed systems with interval time-varying delays

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method

Extremum Seeking-based Iterative Learning Linear MPC

In this work we study the problem of adaptive MPC for linear time-invariant uncertain models. We assume linear models with parametric uncertainties, and propose an iterative multi-variable extremum seeking (MES)-based learning MPC algorithm to learn on-line the uncertain parameters and update the MPC model. We show the effectiveness of this algorithm on a DC servo motor control example.Comment: To appear at the IEEE MSC 201