Analysis and design of quadratically bounded QPV control systems

© 2019. ElsevierA nonlinear system is said to be quadratically bounded (QB) if all its solutions are bounded and this is guaranteed using a quadratic Lyapunov function. This paper considers the QB analysis and state-feedback controller design problems for quadratic parameter varying (QPV) systems. The developed approach, which relies on a linear matrix inequality (LMIs) feasibility problem, ensures that the QB property holds for an invariant ellipsoid which contains a predefined polytopic region of the state space. An example is used to illustrate the main characteristics of the proposed approach and to confirm the validity of the theoretical results.Peer ReviewedPostprint (author's final draft

Optimal state observation using quadratic boundedness: application to UAV disturbance estimation

This paper presents the design of a state observer which guarantees quadratic boundedness of the estimation error. By using quadratic Lyapunov stability analysis, the convergence rate and the ultimate (steady-state) error bounding ellipsoid are identified as the parameters that define the behaviour of the estimation. Then, it is shown that these objectives can be merged in a scalarised objective function with one design parameter, making the design problem convex. In the second part of the article, a UAV model is presented which can be made linear by considering a particular state and frame of reference. The UAV model is extended to incorporate a disturbance model of variable size. The joint model matches the structure required to derive an observer, following the lines of the proposed design approach. An observer for disturbances acting on the UAV is derived and the analysis of the performances with respect to the design parameters is presented. The effectiveness and main characteristics of the proposed approach are shown using simulation results.Peer ReviewedPostprint (author's final draft

Model Prediction-Based Approach to Fault Tolerant Control with Applications

Abstract— Fault-tolerant control (FTC) is an integral component in industrial processes as it enables the system to continue robust operation under some conditions. In this paper, an FTC scheme is proposed for interconnected systems within an integrated design framework to yield a timely monitoring and detection of fault and reconfiguring the controller according to those faults. The unscented Kalman filter (UKF)-based fault detection and diagnosis system is initially run on the main plant and parameter estimation is being done for the local faults. This critical information\ud is shared through information fusion to the main system where the whole system is being decentralized using the overlapping decomposition technique. Using this parameter estimates of decentralized subsystems, a model predictive control (MPC) adjusts its parameters according to the\ud fault scenarios thereby striving to maintain the stability of the system. Experimental results on interconnected continuous time stirred tank reactors (CSTR) with recycle and quadruple tank system indicate that the proposed method is capable to correctly identify various faults, and then controlling the system under some conditions

Model-Based Fault Detection and Estimation for Linear Time Invariant and Piecewise Affine Systems by Using Quadratic Boundedness

Quadratic boundedness is a notion of stability that is adopted to investigate the design of observers for dynamic systems subject to bounded disturbances. We will show how to exploit such observers for the purpose of fault detection. Toward this end, first of all we present the naive application of quadratic boundedness to construct state observers for linear time-invariant systems with state augmentation, i.e., where additional variables may be introduced to account for the occurrence of a fault. Then a Luenberger observer is designed to estimate the augmented state variable of the system in such a way to detect the fault by using a convenient threshold selection. Finally, such an approach is extended to piecewise affine systems by presenting a hybrid Luenberger observer and its related design based on quadratic boundedness. The design of all the observers for both linear time-invariant and piecewise affine systems can be done by using linear matrix inequalities. Simulation results are provided to show the effectiveness of the proposed approach

Optimal control and robust estimation for ocean wave energy converters

This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.Open Acces

Stochastic output feedback MPC with intermittent observations

This paper considers constrained linear systems with stochastic additive disturbances and noisy measurements transmitted over a lossy communication channel. We propose a model predictive control (MPC) law that minimises a discounted cost subject to a discounted expectation constraint. Sensor data is assumed to be lost with known probability, and data losses are accounted for by expressing the predicted control policy as an affine function of future observations, which results in a convex optimal control problem. An online constraint-tightening technique ensures recursive feasibility of the online optimisation problem and satisfaction of the expectation constraint without imposing bounds on the distributions of the noise and disturbance inputs. The discounted cost evaluated along trajectories of the closed loop system is shown to be bounded by the initial optimal predicted cost. We also provide conditions under which the averaged undiscounted closed loop cost accumulated over an infinite horizon is bounded. Numerical simulations are described to illustrate these results.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:2004.0259

Adaptive Optimal Control The Thinking Man's GPC

Exploring connections between adaptive control theory and practice, this book treats the techniques of linear quadratic optimal control and estimation (Kalman filtering), recursive identification, linear systems theory and robust arguments

Vehicle yaw motion control using takagi-sugeno modeling and quadratic boundedness via dynamic output feedback

International audienceThis paper presents the design and the simulation test of a Takagi-Sugeno (TS) fuzzy output feedback for yaw motion control. An integrated steering and differential braking controller based on invariant sets, quadratic boundedness theory and a common Lyapunov function has been developed. The TS fuzzy model is able to handle elegantly the nonlinear behavior the vehicle lateral dynamics. The computation of the control law has been achieved using Linear and Bilinear Matrix Inequalities (LMI-BMI) methods. Simulation test shows the controlled car is able to achieve the ISO3888-2 transient maneuver. Some design parameters can be adjusted to handle the tradeoff between safety constraints and comfort specifications