Analysis and Design of Singular Markovian Jump Systems

This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H? control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques. Features of the book include: · study of the stability problem for SMJSs with general transition rate matrices (TRMs); · stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; · mode-dependent and mode-independent H? control solutions with development of a type of disordered controller; · observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; · consideration of robust H? filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering · development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corresponding closed-loop system states · applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course

Enhanced Principles in Design of Adaptive Fault Observers

In this chapter, modified techniques for fault estimation in linear dynamic systems are proposed, which give the possibility to simultaneously estimate the system state as well as slowly varying faults. Using the continuous-time adaptive observer form, the considered faults are assumed to be additive, thereby the principles can be applied for a broader class of fault signals. Enhanced algorithms using H∞ approach are provided to verify stability of the observers, giving algorithms with improved performance of fault estimation. Exploiting the procedure for transforming the model with additive faults into an extended form, the proposed technique allows to obtain fault estimates that can be used for fault compensation in the fault tolerant control scheme. Analyzing the ambit of performances given on the mixed H2/H∞ design of the fault tolerant control, the joint design conditions are formulated as a minimization problem subject to convex constraints expressed by a system of linear matrix inequalities. Applied enhanced design conditions increase estimation rapidity also in noise environment and formulate a general framework for fault estimation using augmented or adaptive observer structures and active fault tolerant control in linear dynamic systems

Adaptive observer for state variables of a time-varying nonlinear system with unknown constant parameters and delayed measurements

Unknown constant parameters estimation problem for a nonlinear time-varying system with delayed measurements is considered. The objective of this work is to design an adaptive observer for a nonlinear time-varying system. The observer must provide asymptotic convergence of the unknown constant parameters estimates to their true values. The main idea behind the method is to perform the parametrization of initial dynamical system based on GPEBO (Generalized Parameter Estimation Based Observer) technology and to build a linear regression model. The identification of linear regression model unknown parameters is performed using least square method with forgetting factor. This work develops the previously published approach for the case of nonlinear time-varying systems with delayed measurements. New parameters estimation algorithm can be applied for technical tasks, such as technical condition control and automatic control systems design

Adaptive Data-Driven Control for Linear Time Varying Systems

In this paper, we propose an adaptive data-driven control approach for linear time varying systems, affected by bounded measurement noise. The plant to be controlled is assumed to be unknown, and no information in regard to its time varying behaviour is exploited. First, using set-membership identification techniques, we formulate the controller design problem through a model-matching scheme, i.e., designing a controller such that the closed-loop behaviour matches that of a given reference model. The problem is then reformulated as to derive a controller that corresponds to the minimum variation bounding its parameters. Finally, a convex relaxation approach is proposed to solve the formulated controller design problem by means of linear programming. The effectiveness of the proposed scheme is demonstrated by means of two simulation examples

Synthesis and control of generalised dynamically substructured systems

The experimental technique for testing engineering systems via the method of dynamic substructuring is receiving significant global interest, for example in the fields of large-scale structural, aerospace, and automotive system testing. Dynamically substructured systems (DSSs) enable full-size, critical components of a complete system to be physically tested in real-time, within a laboratory environment, while the remainder of the system is modelled numerically. The intention is that the combined physical-numerical DSS behaves as if it were the complete (or emulated) system.In an ideal mechanical DSS, for example, perfect synchronization of displacements and forces at the interfaces between the numerical and physical components (or substructures) is required. Hence, a key design feature of successful DSS systems is the high fidelity of the control action. Equally, a DSS controller must be able to cope with non-linear, time-varying, and uncertain parameters within the physical substructure dynamics.The main purpose of this paper is to present a generalized DSS framework, together with associated linear and adaptive control strategies, that are specifically tailored to achieve high synchronization performance. The initial studies of this problem, as described in an earlier paper by Stoten and Hyde, are therefore continued by generalizing both the DSS dynamics and the control strategies to include (a) a number of newly defined modes of operation and (b) multivariable dynamics. In addition, comparative implementation and simulation studies are included, based upon the DSS testing of a mechanical system (a planar quasi-motorcycle rig), which was specifically designed to highlight the main features of this research. The comparative studies show that excellent DSS control can be achieved, especially with the addition of an adaptive component to the controller, despite significant changes to the physical substructure dynamics

Adaptive and Optimal Motion Control of Multi-UAV Systems

This thesis studies trajectory tracking and coordination control problems for single and multi unmanned aerial vehicle (UAV) systems. These control problems are addressed for both quadrotor and fixed-wing UAV cases. Despite the fact that the literature has some approaches for both problems, most of the previous studies have implementation challenges on real-time systems. In this thesis, we use a hierarchical modular approach where the high-level coordination and formation control tasks are separated from low-level individual UAV motion control tasks. This separation helps efficient and systematic optimal control synthesis robust to effects of nonlinearities, uncertainties and external disturbances at both levels, independently. The modular two-level control structure is convenient in extending single-UAV motion control design to coordination control of multi-UAV systems. Therefore, we examine single quadrotor UAV trajectory tracking problems to develop advanced controllers compensating effects of nonlinearities and uncertainties, and improving robustness and optimality for tracking performance. At fi rst, a novel adaptive linear quadratic tracking (ALQT) scheme is developed for stabilization and optimal attitude control of the quadrotor UAV system. In the implementation, the proposed scheme is integrated with Kalman based reliable attitude estimators, which compensate measurement noises. Next, in order to guarantee prescribed transient and steady-state tracking performances, we have designed a novel backstepping based adaptive controller that is robust to effects of underactuated dynamics, nonlinearities and model uncertainties, e.g., inertial and rotational drag uncertainties. The tracking performance is guaranteed to utilize a prescribed performance bound (PPB) based error transformation. In the coordination control of multi-UAV systems, following the two-level control structure, at high-level, we design a distributed hierarchical (leader-follower) 3D formation control scheme. Then, the low-level control design is based on the optimal and adaptive control designs performed for each quadrotor UAV separately. As particular approaches, we design an adaptive mixing controller (AMC) to improve robustness to varying parametric uncertainties and an adaptive linear quadratic controller (ALQC). Lastly, for planar motion, especially for constant altitude flight of fixed-wing UAVs, in 2D, a distributed hierarchical (leader-follower) formation control scheme at the high-level and a linear quadratic tracking (LQT) scheme at the low-level are developed for tracking and formation control problems of the fixed-wing UAV systems to examine the non-holonomic motion case. The proposed control methods are tested via simulations and experiments on a multi-quadrotor UAV system testbed

Stability Assessment and Tuning of an Adaptively Augmented Classical Controller for Launch Vehicle Flight Control

Recently, a robust and practical adaptive control scheme for launch vehicles [ [1] has been introduced. It augments a classical controller with a real-time loop-gain adaptation, and it is therefore called Adaptive Augmentation Control (AAC). The loop-gain will be increased from the nominal design when the tracking error between the (filtered) output and the (filtered) command trajectory is large; whereas it will be decreased when excitation of flex or sloshing modes are detected. There is a need to determine the range and rate of the loop-gain adaptation in order to retain (exponential) stability, which is critical in vehicle operation, and to develop some theoretically based heuristic tuning methods for the adaptive law gain parameters. The classical launch vehicle flight controller design technics are based on gain-scheduling, whereby the launch vehicle dynamics model is linearized at selected operating points along the nominal tracking command trajectory, and Linear Time-Invariant (LTI) controller design techniques are employed to ensure asymptotic stability of the tracking error dynamics, typically by meeting some prescribed Gain Margin (GM) and Phase Margin (PM) specifications. The controller gains at the design points are then scheduled, tuned and sometimes interpolated to achieve good performance and stability robustness under external disturbances (e.g. winds) and structural perturbations (e.g. vehicle modeling errors). While the GM does give a bound for loop-gain variation without losing stability, it is for constant dispersions of the loop-gain because the GM is based on frequency-domain analysis, which is applicable only for LTI systems. The real-time adaptive loop-gain variation of the AAC effectively renders the closed-loop system a time-varying system, for which it is well-known that the LTI system stability criterion is neither necessary nor sufficient when applying to a Linear Time-Varying (LTV) system in a frozen-time fashion. Therefore, a generalized stability metric for time-varying loop=gain perturbations is needed for the AAC