Robust explicit model predictive control for hybrid linear systems with parameter uncertainties

Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments

Linear matrix inequality-based nonlinear adaptive robust control with application to unmanned aircraft systems

Unmanned aircraft systems (UASs) are gaining popularity in civil and commercial applications as their lightweight on-board computers become more powerful and affordable, their power storage devices improve, and the Federal Aviation Administration addresses the legal and safety concerns of integrating UASs in the national airspace. Consequently, many researchers are pursuing novel methods to control UASs in order to improve their capabilities, dependability, and safety assurance. The nonlinear control approach is a common choice as it offers several benefits for these highly nonlinear aerospace systems (e.g., the quadrotor). First, the controller design is physically intuitive and is derived from well known dynamic equations. Second, the final control law is valid in a larger region of operation, including far from the equilibrium states. And third, the procedure is largely methodical, requiring less expertise with gain tuning, which can be arduous for a novice engineer. ^ Considering these facts, this thesis proposes a nonlinear controller design method that combines the advantages of adaptive robust control (ARC) with the powerful design tools of linear matrix inequalities (LMI). The ARC-LMI controller is designed with a discontinuous projection-based adaptation law, and guarantees a prescribed transient and steady state tracking performance for uncertain systems in the presence of matched disturbances. The norm of the tracking error is bounded by a known function that depends on the controller design parameters in a known form. Furthermore, the LMI-based part of the controller ensures the stability of the system while overcoming polytopic uncertainties, and minimizes the control effort. This can reduce the number of parameters that require adaptation, and helps to avoid control input saturation. ^ These desirable characteristics make the ARC-LMI control algorithm well suited for the quadrotor UAS, which may have unknown parameters and may encounter external disturbances such as wind gusts and turbulence. This thesis develops the ARC-LMI attitude and position controllers for an X-configuration quadrotor helicopter. The inner-loop of the autopilot controls the attitude and altitude of the quadrotor, and the outer-loop controls its position in the earth-fixed coordinate frame. Furthermore, by intelligently generating a smooth trajectory from the given reference coordinates (waypoints), the transient performance is improved. The simulation results indicate that the ARC-LMI controller design is useful for a variety of quadrotor applications, including precise trajectory tracking, autonomous waypoint navigation in the presence of disturbances, and package delivery without loss of performanc

Observer-based robust fault estimation for fault-tolerant control

A control system is fault-tolerant if it possesses the capability of optimizing the system stability and admissible performance subject to bounded faults, complexity and modeling uncertainty. Based on this definition this thesis is concerned with the theoretical developments of the combination of robust fault estimation (FE) and robust active fault tolerant control (AFTC) for systems with both faults and uncertainties.This thesis develops robust strategies for AFTC involving a joint problem of on-line robust FE and robust adaptive control. The disturbances and modeling uncertainty affect the FE and FTC performance. Hence, the proposed robust observer-based fault estimator schemes are combined with several control methods to achieve the desired system performance and robust active fault tolerance. The controller approaches involve concepts of output feedback control, adaptive control, robust observer-based state feedback control. A new robust FE method has been developed initially to take into account the joint effect of both fault and disturbance signals, thereby rejecting the disturbances and enhancing the accuracy of the fault estimation. This is then extended to encompass the robustness with respect to modeling uncertainty.As an extension to the robust FE and FTC scheme a further development is made for direct application to smooth non-linear systems via the use of linear parameter-varying systems (LPV) modeling.The main contributions of the research are thus:- The development of a robust observer-based FE method and integration design for the FE and AFTC systems with the bounded time derivative fault magnitudes, providing the solution based on linear matrix inequality (LMI) methodology. A stability proof for the integrated design of the robust FE within the FTC system.- An improvement is given to the proposed robust observer-based FE method and integrated design for FE and AFTC systems under the existence of different disturbance structures.- New guidance for the choice of learning rate of the robust FE algorithm.- Some improvement compared with the recent literature by considering the FTC problem in a more general way, for example by using LPV modeling

Multiple-Model Robust Adaptive Vehicle Motion Control

An improvement in active safety control systems has become necessary to assist drivers in unfavorable driving conditions. In these conditions, the dynamic of the vehicle shows rather different respond to driver command. Since available sensor technologies and estimation methods are insufficient, uncertain nonlinear tire characteristics and road condition may not be correctly figured out. Thus, the controller cannot provide the appropriate feedback input to vehicle, which may result in deterioration of controller performance and even in loss of vehicle control. These problems have led many researchers to new active vehicle stability controllers which make vehicle robust against critical driving conditions like harsh maneuvers in which tires show uncertain nonlinear behaviour and/or the tire-road friction coefficient is uncertain and low. In this research, the studied vehicle has active front steering system for driver steer correction and in-wheel electric motors in all wheels to generate torque vector at vehicle center of gravity. To address robustness against uncertain nonlinear characteristics of tire and road condition, new blending based multiple-model adaptive schemes utilizing gradient and recursive least squares (RLS) methods are proposed for a faster system identification. To this end, the uncertain nonlinear dynamics of vehicle motion is addressed as a multiple-input multiple-output (MIMO) linear system with polytopic parameter uncertainties. These polytopic uncertainties denote uncertain variation in tire longitudinal and lateral force capacity due to nonlinear tire characteristics and road condition. In the proposed multiple-model approach, a set of fixed linear parametric identifi cation models are designed in advance, based on the known bounds of polytopic parameter set. The proposed adaptive schemes continuously generates a weighting vector for blending the identifi cation model to achieve the true model (operation condition) of the vehicle. Furthermore, the proposed adaptive schemes are generalized for MIMO systems with polytopic parameter uncertainties. The asymptotic stability of the proposed adaptive identifi cation schemes for linear MIMO systems is studied in detail. Later, the proposed blending based adaptive identi fication schemes are used to develop Linear Quadratic (LQ) based multiple-model adaptive control (MMAC) scheme for MIMO systems with polytopic parameter uncertainties. To this end, for each identi fication model, an optimal LQ controller is computed on-line for the corresponding model in advance, which saves computation power during operation. The generated control inputs from the set of LQ controllers is being blended on-line using weighting vector continuously updated by the proposed adaptive identifi cation schemes. The stability analysis of the proposed LQ based optimal MMAC scheme is provided. The developed LQ based optimal MMAC scheme has been applied to motion control of the vehicle. The simulation application to uncertain lateral single-track vehicle dynamics is presented in Simulink environment. The performances of the proposed LQ based MMAC utilizing RLS and gradient based methods have been compared to each other and an LQ controller which is designed using the same performance matrices and fixed nominal values of the uncertain parameters. The results validated the stability and effectiveness of the proposed LQ based MMAC algorithm and demonstrate that the proposed adaptive LQ control schemes outperform over the LQ control scheme for tracking tasks. In the next step, we addressed the constraints on actuation systems for a model predictive control (MPC) based MMAC design. To determine the constraints on torque vectoring at vehicle center of gravity (CG), we have used the min/max values of torque and torque rate at each corner, and the vehicle kinematic structure information. The MPC problem has been redefi ned as a constrained quadratic programming (QP) problem which is solved in real-time via interior-point algorithm by an embedded QP solver using MATLAB each time step. The solution of the designed MPC based MMAC provides total steering angle and desired torque vector at vehicle CG which is optimally distributed to each corner based on holistic corner control (HCC) principle. For validation of the designed MPC based MMAC scheme, several critical driving scenarios has been simulated using a high- fidelity vehicle simulation environment CarSim/Simulink. The performance of the proposed MPC based MMAC has been compared to an MPC controller which is designed for a wet road condition using the same tuning parameters in objective function design. The results validated the stability and effectiveness of the proposed MPC based MMAC algorithm and demonstrate that the proposed adaptive control scheme outperform over an MPC controller with fixed parameter values for tracking tasks

Robust data-based predictive control of systems with parametric uncertainties: Paving the way for cooperative learning

This article combines data and tube-based predictive control to deal with systems with bounded parametric uncertainty. This integration generates robustly feasible control sequences that can also be exploited in cooperative scenarios where controllers learn from each other’s data. In particular, the approach is based on a database that contains information from previous executions of the same and other controllers handling similar systems. By the combination of feasible histories plus an auxiliary control law that deals with bounded uncertainties, which only needs to be stabilizing for at least one of the system realizations within the uncertainty set, this scheme provides a finite-horizon predictive controller that guarantees exponential stability and robust constraint satisfaction. The validity and benefits of the proposed scheme are shown in case studies with linear and non-linear dynamics.Unión Europea : OCONTSOLAR (ref. 789051)Ministerio de Ciencia e Innovación PID2020-119476RB-I00Ministerio de Ciencia e Innovación PID2022- 141159OB-I0