Min–max MPC using a tractable QP problem

Min–max model predictive controllers (MMMPC) suffer from a great computational burden that is often circumvented by using approximate solutions or upper bounds of the worst possible case of a performance index. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min–max problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the min–max problem and the resulting control is shown to have a guaranteed stability. A simulation example is given in the paper

Stochastic model predictive control of LPV systems via scenario optimization

A stochastic receding-horizon control approach for constrained Linear Parameter Varying discrete-time systems is proposed in this paper. It is assumed that the time-varying parameters have stochastic nature and that the system's matrices are bounded but otherwise arbitrary nonlinear functions of these parameters. No specific assumption on the statistics of the parameters is required. By using a randomization approach, a scenario-based finite-horizon optimal control problem is formulated, where only a finite number M of sampled predicted parameter trajectories (‘scenarios') are considered. This problem is convex and its solution is a priori guaranteed to be probabilistically robust, up to a user-defined probability level p. The p level is linked to M by an analytic relationship, which establishes a tradeoff between computational complexity and robustness of the solution. Then, a receding horizon strategy is presented, involving the iterated solution of a scenario-based finite-horizon control problem at each time step. Our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time, either deterministically, or with probability no smaller than p. The features of the approach are illustrated by a numerical example

Model Predictive Control of stochastic LPV Systems via Random Convex Programs

This paper considers the problem of stabilization of stochastic Linear Parameter Varying (LPV) discrete time systems in the presence of convex state and input constraints. By using a randomization approach, a convex finite horizon optimal control problem is derived, even when the dependence of the system's matrices on the time-varying parameters is nonlinear. This convex problem can be solved efficiently, and its solution is a-priori guaranteed to be probabilistically robust, up to a user-defined probability level p. Then, a novel receding horizon control strategy that involves, at each time step, the solution of a finite-horizon scenario-based control problem, is proposed. It is shown that the resulting closed loop scheme drives the state to a terminal set in finite time, either deterministically, or with probability no less than p. The features of the approach are shown through a numerical exampl

Predictive control approaches to fault tolerant control of wind turbines

This thesis focuses on active fault tolerant control (AFTC) of wind turbine systems. Faults in wind turbine systems can be in the form of sensor faults, actuator faults, or component faults. These faults can occur in different locations, such as the wind speed sensor, the generator system, drive train system or pitch system. In this thesis, some AFTC schemes are proposed for wind turbine faults in the above locations. Model predictive control (MPC) is used in these schemes to design the wind turbine controller such that system constraints and dual control goals of the wind turbine are considered. In order to deal with the nonlinearity in the turbine model, MPC is combined with Takagi-Sugeno (T-S) fuzzy modelling. Different fault diagnosis methods are also proposed in different AFTC schemes to isolate or estimate wind turbine faults.The main contributions of the thesis are summarized as follows:A new effective wind speed (EWS) estimation method via least-squares support vector machines (LSSVM) is proposed. Measurements from the wind turbine rotor speed sensor and the generator speed sensor are utilized by LSSVM to estimate the EWS. Following the EWS estimation, a wind speed sensor fault isolation scheme via LSSVM is proposed.A robust predictive controller is designed to consider the EWS estimation error. This predictive controller serves as the baseline controller for the wind turbine system operating in the region below rated wind speed.T-S fuzzy MPC combining MPC and T-S fuzzy modelling is proposed to design the wind turbine controller. MPC can deal with wind turbine system constraints externally. On the other hand, T-S fuzzy modelling can approximate the nonlinear wind turbine system with a linear time varying (LTV) model such that controller design can be based on this LTV model. Therefore, the advantages of MPC and T-S fuzzy modelling are both preserved in the proposed T-S fuzzy MPC.A T-S fuzzy observer, based on online eigenvalue assignment, is proposed as the sensor fault isolation scheme for the wind turbine system. In this approach, the fuzzy observer is proposed to deal with the nonlinearity in the wind turbine system and estimate system states. Furthermore, the residual signal generated from this fuzzy observer is used to isolate the faulty sensor.A sensor fault diagnosis strategy utilizing both analytical and hardware redundancies is proposed for wind turbine systems. This approach is proposed due to the fact that in the real application scenario, both analytical and hardware redundancies of wind turbines are available for designing AFTC systems.An actuator fault estimation method based on moving horizon estimation (MHE) is proposed for wind turbine systems. The estimated fault by MHE is then compensated by a T-S fuzzy predictive controller. The fault estimation unit and the T-S fuzzy predictive controller are combined to form an AFTC scheme for wind turbine actuator faults

Trajectory planning for unmanned vehicles using robust receding horizon control

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (p. 211-223).This thesis presents several trajectory optimization algorithms for a team of cooperating unmanned vehicles operating in an uncertain and dynamic environment. The first, designed for a single vehicle, is the Robust Safe But Knowledgeable (RSBK) algorithm, which combines several previously published approaches to recover the main advantages of each. This includes a sophisticated cost-to-go function that provides a good estimate of the path beyond the planning horizon, which is extended in this thesis to account for three dimensional motion; constraint tightening to ensure robustness to disturbances, which is extended to a more general class of disturbance rejection controllers compared to the previous work, with a new off-line design procedure; and a robust invariant set which ensures the safety of the vehicle in the event of environmental changes beyond the planning horizon. The system controlled by RSBK is proven to robustly satisfy all vehicle and environmental constraint under the action of bounded external disturbances. Multi-vehicle teams could also be controlled using centralized RSBK, but to reduce computational effort, several distributed algorithms are presented in this thesis. The main challenge in distributing the planning is to capture the complex couplings between vehicles.(cont.) A decentralized form of RSBK algorithm is developed by having each vehicle optimize over its own decision variables and then locally communicate the solutions to its neighbors. By integrating a grouping algorithm, this approach enables simultaneous computation by vehicles in the team while guaranteeing the robust feasibility of the entire fleet. The use of a short planning horizon within RSBK enables the use of a very simple initialization algorithm when compared to previous work, which is essential if the technique is to be used in dynamic and uncertain environments. Improving the level of cooperation between the vehicles is another challenge for decentralized planning, but this thesis presents a unique strategy by enabling each vehicle to optimize its own decision as well as a feasible perturbation of its neighboring vehicles' plans. The resulting cooperative form of the distributed RSBK is shown to result in solutions that sacrifice local performance if it benefits the overall team performance. This desirable performance improvement is achieved with only a small increase in the computation and communication requirements. These algorithms are tested and demonstrated in simulation and on two multi-vehicle testbeds using rovers and quadrotors.(cont.) The experimental results demonstrate that the proposed algorithms successfully overcome the implementation challenges, such as limited onboard computation and communication resources, as well as the various sources of real-world uncertainties arising from modeling error of the vehicle dynamics, tracking error of the low-level controller, external disturbance, and sensing noise.by Yoshiaki Kuwata.Ph.D