A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Decentralised adaptive control of a class of hidden leader–follower non-linearly parameterised coupled MASs

In this study, decentralised adaptive control is investigated for a class of discrete-time non-linear hidden leader–follower multi-agent systems (MASs). Different from the conventional leader–follower MAS, among all the agents, there exists a hidden leader that knows the desired reference trajectory, while the follower agents know neither the desired reference signal nor which is a leader agent. Each agent is affected from the history information of its own neighbours. The dynamics of each agent is described by the non-linear discrete-time auto-regressive model with unknown parameters. In order to deal with the uncertainties and non-linearity, a projection algorithm is applied to estimate the unknown parameters. Based on the certainty equivalence principle in adaptive control theory, the control for the hidden leader agent is designed by the desired reference signal, and the local control for each follower agent is designed using neighbourhood history information. Under the decentralised adaptive control, rigorous mathematical proofs are provided to show that the hidden leader agent tracks the desired reference signal, all the follower agents follow the hidden leader agent, and the closed-loop system eventually achieves strong synchronisation in the presence of strong couplings. In the end, the simulation results show the validity of this scheme

Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays

The stabilization of uncertain LTI/LPV time delay systems with time varying delays by state-feedback controllers is addressed. At the difference of other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the $\mathcal{H}_\infty$ performance measure is considered. The interest of the approach is finally illustrated through several examples

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one model to identify all switching states of the regression is used in the developed procedure with the following two-fold contribution. First of all, we propose a new truly online estimation algorithm based on a well-known DREM approach to detect switching time and preserve time alertness with adjustable detection delay. Secondly, despite the fact that a switching signal function is unknown, the adaptive law is derived that provides global exponential convergence of the regression parameters to their true values in case the regressor is finitely exciting somewhere inside the time interval between two consecutive parameters switches. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved. Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second-order plant model are used.Comment: 31 pages, 12 figure

Nonlinear Control and Estimation Techniques with Applications to Vision-based and Biomedical Systems

This dissertation is divided into four self-contained chapters. In Chapter 1, a new estimator using a single calibrated camera mounted on a moving platform is developed to asymptotically recover the range and the three-dimensional (3D) Euclidean position of a static object feature. The estimator also recovers the constant 3D Euclidean coordinates of the feature relative to the world frame as a byproduct. The position and orientation of the camera is assumed to be measurable unlike existing observers where velocity measurements are assumed to be known. To estimate the unknown range variable, an adaptive least squares estimation strategy is employed based on a novel prediction error formulation. A Lyapunov stability analysis is used to prove the convergence properties of the estimator. The developed estimator has a simple mathematical structure and can be used to identify range and 3D Euclidean coordinates of multiple features. These properties of the estimator make it suitable for use with robot navigation algorithms where position measurements are readily available. Numerical simulation results along with experimental results are presented to illustrate the effectiveness of the proposed algorithm. In Chapter 2, a novel Euclidean position estimation technique using a single uncalibrated camera mounted on a moving platform is developed to asymptotically recover the three-dimensional (3D) Euclidean position of static object features. The position of the moving platform is assumed to be measurable, and a second object with known 3D Euclidean coordinates relative to the world frame is considered to be available a priori. To account for the unknown camera calibration parameters and to estimate the unknown 3D Euclidean coordinates, an adaptive least squares estimation strategy is employed based on prediction error formulations and a Lyapunov-type stability analysis. The developed estimator is shown to recover the 3D Euclidean position of the unknown object features despite the lack of knowledge of the camera calibration parameters. Numerical simulation results along with experimental results are presented to illustrate the effectiveness of the proposed algorithm. In Chapter 3, a new range identification technique for a calibrated paracatadioptric system mounted on a moving platform is developed to recover the range information and the three-dimensional (3D) Euclidean coordinates of a static object feature. The position of the moving platform is assumed to be measurable. To identify the unknown range, first, a function of the projected pixel coordinates is related to the unknown 3D Euclidean coordinates of an object feature. This function is nonlinearly parameterized (i.e., the unknown parameters appear nonlinearly in the parameterized model). An adaptive estimator based on a min-max algorithm is then designed to estimate the unknown 3D Euclidean coordinates of an object feature relative to a fixed reference frame which facilitates the identification of range. A Lyapunov-type stability analysis is used to show that the developed estimator provides an estimation of the unknown parameters within a desired precision. Numerical simulation results are presented to illustrate the effectiveness of the proposed range estimation technique. In Chapter 4, optimization of antiangiogenic therapy for tumor management is considered as a nonlinear control problem. A new technique is developed to optimize antiangiogenic therapy which minimizes the volume of a tumor and prevents it from growing using an optimum drug dose. To this end, an optimum desired trajectory is designed to minimize a performance index. Two controllers are then presented that drive the tumor volume to its optimum value. The first controller is proven to yield exponential results given exact model knowledge. The second controller is developed under the assumption of parameteric uncertainties in the system model. A least-squares estimation strategy based on a prediction error formulation and a Lyapunov-type stability analysis is developed to estimate the unknown parameters of the performance index. An adaptive controller is then designed to track the desired optimum trajectory. The proposed tumor minimization scheme is shown to minimize the tumor volume with an optimum drug dose despite the lack of knowledge of system parameters. Numerical simulation results are presented to illustrate the effectiveness of the proposed technique. An extension of the developed technique for a mathematical model which accounts for pharmacodynamics and pharmacokinetics is also presented. Futhermore, a technique for the estimation of the carrying capacity of endothelial cells is also presented

Adaptive control of sinusoidal brushless DC motor actuators

Electrical Power Assisted Steering system (EPAS) will likely be used on future automotive power steering systems. The sinusoidal brushless DC (BLDC) motor has been identified as one of the most suitable actuators for the EPAS application. Motor characteristic variations, which can be indicated by variations of the motor parameters such as the coil resistance and the torque constant, directly impart inaccuracies in the control scheme based on the nominal values of parameters and thus the whole system performance suffers. The motor controller must address the time-varying motor characteristics problem and maintain the performance in its long service life. In this dissertation, four adaptive control algorithms for brushless DC (BLDC) motors are explored. The first algorithm engages a simplified inverse dq-coordinate dynamics controller and solves for the parameter errors with the q-axis current (iq) feedback from several past sampling steps. The controller parameter values are updated by slow integration of the parameter errors. Improvement such as dynamic approximation, speed approximation and Gram-Schmidt orthonormalization are discussed for better estimation performance. The second algorithm is proposed to use both the d-axis current (id) and the q-axis current (iq) feedback for parameter estimation since id always accompanies iq. Stochastic conditions for unbiased estimation are shown through Monte Carlo simulations. Study of the first two adaptive algorithms indicates that the parameter estimation performance can be achieved by using more history data. The Extended Kalman Filter (EKF), a representative recursive estimation algorithm, is then investigated for the BLDC motor application. Simulation results validated the superior estimation performance with the EKF. However, the computation complexity and stability may be barriers for practical implementation of the EKF. The fourth algorithm is a model reference adaptive control (MRAC) that utilizes the desired motor characteristics as a reference model. Its stability is guaranteed by Lyapunov’s direct method. Simulation shows superior performance in terms of the convergence speed and current tracking. These algorithms are compared in closed loop simulation with an EPAS model and a motor speed control application. The MRAC is identified as the most promising candidate controller because of its combination of superior performance and low computational complexity. A BLDC motor controller developed with the dq-coordinate model cannot be implemented without several supplemental functions such as the coordinate transformation and a DC-to-AC current encoding scheme. A quasi-physical BLDC motor model is developed to study the practical implementation issues of the dq-coordinate control strategy, such as the initialization and rotor angle transducer resolution. This model can also be beneficial during first stage development in automotive BLDC motor applications

Adaptive neural control of nonlinear systems with hysteresis

Ph.DDOCTOR OF PHILOSOPH