Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques

Disturbance observer enhanced neural network LPV control for a blended-wing-body large aircraft

The problem of trajectory tracking control for a Blended-Wing-Body (BWB) large aircraft with model parameter uncertainties and unknown disturbances is considered. A Linear Parameter-Varying (LPV) model is derived from the nonlinear dynamics of the BWB aircraft from which a robust linear parameter-varying controller is designed to track a desired trajectory. Using a Single Quadratic Lyapunov Function (SQLF) and an infinite number of linear matrix inequalities to be evaluated at all vertices, a pair of positive definite symmetric matrix solutions is determined via Lyapunov stability theory and linear matrix inequality technique. Furthermore, a disturbance-observer is designed to process the unknown disturbances. Considering the plant exists some model errors except for disturbances, a Radial Basis Function Neural Network (RBFNN) approximation is embedded into the SQLF LPV controller to improve tracking performances, and a composite disturbance-observer based Neural Network Single Quadratic Lyapunov Function (NNSQLF) controller can realize desired trajectory tracking of the linear parameter-varying system through regulating performance weighting functions. The closed-loop system of trajectory tracking control is proved to be asymptotically stable by using Lyapunov theory. Simulation results of forward flight speed and altitude tracking control of the BWB aircraft show that the proposed disturbance-observer based NNSQLF control can robustly stabilize the LPV system and precisely track the desired trajectory by comparing with conventional SQLF control and Parameter-Dependent Lyapunov Functions (PDLF) control, even in unknown exterior disturbances and model uncertainties

Robust gain-scheduled H [infinity] control for unmanned aerial vehicles

This thesis considers the problem of the design of robust gain-scheduled ight controllers for conventional xed-wing unmanned aerial vehicles (UAVs). The design approaches employ a linear parameter-varying (LPV) control technique, that is based on the principle of the gain-scheduled output feedback H1 control, because a conventional gain-scheduling technique is both expensive and time-consuming for many UAV applications. In addition, importantly, an LPV controller can guarantee the stability, robustness and performance properties of the closed-loop system across the full or de ned ight envelope. A ight control application problem for conventional xed-wing UAVs is considered in this thesis. This is an autopilot design (i.e. speed-hold, altitude-hold, and heading-hold) that is used to demonstrate the impacts of the proposed scheme in robustness and performance improvement of the ight controller design over a fuller range of ight conditions. The LPV ight controllers are synthesized using single quadratic (SQLF) or parameterdependent (PDLF) Lyapunov functions where the synthesis problems involve solving the linear matrix inequality (LMI) constraints that can be e ciently solved using standard software. To synthesize an LPV autopilot of a Jindivik UAV, the longitudinal and lateral LPV models are required in which they are derived from a six degree-of-fredoom (6-DOF) nonlinear model of the vehicle using Jacobian linearization. However, the derived LPV models are nonlinearly dependent on the time-varying parameters, i.e. speed and altitude. To obtain a nite number of LMIs and avoid the gridding parameter technique, the Tensor-Product (TP) model transformation is applied to transform the nonlinearly parameter-dependent LPV model into a TP-type convex polytopic model form. Hence, the gain-scheduled output feedback H1 control technique can be applied to the resulting TP convex polytopic model using the single quadratic Lyapunov functions. The parameter-dependent Lyapunov functions is also used to synthesize another LPV controller that is less conservative than the SQLF-based LPV controller. However, using the parameter-dependent Lyapunov functions involves solving an in nite number of LMIs for which a number of convexifying techniques exist, based on an a ne LPV model, for obtaining a nite number of LMIs. In this thesis, an a ne LPV model is converted from the nonlinearly parameter-dependent LPV model using a minimum least-squares method. In addition, an alternative approach for obtaining a nite number of LMIs is proposed, by simple manipulations on the bounded reallemma inequality, a symmetric matrix polytope inequality form is obtained. Hence, the LMIs need only be evaluated at all vertices. A technique to construct the intermediate controller variables as an a ne matrix-valued function in the polytopic coordinates of the scheduled parameter is also proposed. The time-varying real parametric uncertainties are included in the system statespace model matrices of an a ne LPV model as a linear fractional transformation (LFT) form in order to improve robustness of the designed LPV controllers in the presence of mismatch uncertainties between the nonlinearly parameter-dependent LPV model and the a ne LPV model. Hence, a new class of LPV models is obtained called an uncertain a ne LPV model which is less conservative than the existing parameter-dependent linear fractional transformation model (LPV/LFT). New algorithms of robust stability analysis and gain-scheduled controller synthesis for this uncertain a ne LPV model using single quadratic and parameter-dependent Lyapunov functions are proposed. The analysis and synthesis conditions are represented in the form of a nite number of LMIs. Moreover, the proposed method is applied to synthesize a lateral autopilot, i.e. heading-hold, for a bounded ight envelope of the Jindivik UAV. The simulation results on a full 6-DOF Jindivik nonlinear model are presented to show the e ectiveness of the approach

Gain-scheduled H-infinity control for tensor product type polytopic plants

A tensor product (TP) model transformation is a recently proposed technique for transforming a given linear parameter-varying (LPV) model into polytopic model form, for which there are many methods that can be used for controller design. This paper proposes an alternative approach to the design of a gain-scheduled output feedback H∞ controller with guaranteed L2-gain parameter-dependent performance for a class of TP type polytopic models using parameter-dependent Lyapunov functions where the linear matrix inequalities (LMIs) need only to be evaluated at all vertices of the system state-space model matrices and the variation rate of the scheduled parameters. In addition, a construction technique of the intermediate controller variables is also proposed as a matrix-valued function in the polytopic coordinates of the scheduled parameters. The performance of the proposed approach is tested on a missile autopilot design problem. Furthermore, nonlinear simulation results show the effectiveness of these proposed techniques