The Dynamic Regulation of Linear Discrete-time Systems with Unknown Input (A Design Method Using Adaptive State Observer)

The topic of this paper is the backstepping-based solution of the robust state feedback regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients. Thereby, a large class of outputs is considered, i.e., mixed distributed and pointwise in-domain or boundary outputs. The state feedback regulator design is based on the $\boldsymbol {p}$ -copy internal model principle. This results in a stabilization problem for a cascade of $\boldsymbol {m+p}$ boundary controlled transport partial differential equations (PDEs) with $\boldsymbol {p}$ ordinary differential equations (ODEs). For this, a systematic backstepping approach is presented, in which all design equations are explicitly solvable in backstepping coordinates. Furthermore, the solvability conditions for the considered output regulation problem can be evaluated in closed form utilizing the plant transfer behavior. Robust output regulation is verified for nondestabilizing model uncertainties and unknown disturbance input locations. A $\boldsymbol {4 \times 4}$ hyperbolic system with uncertain transport velocities and couplings in the transport PDEs illustrates the results of this paper.

Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input

The regulator problem for linear uncertain continuous-time systems having control constraints is considered. Necessary and sufficient conditions of positive invariance of polyhedral domains are extended to the case of continuous-time uncertain systems. Robust constrained regulators are then derived. An application to the control of a stirred tank pH is then achieved. First, the process is modeled as models studied hereafter, then a robust constrained regulator is calculated. Simulation results show that this control law is easy to implement and guarantees robust asymptotic stability and control admissibility.

This paper focuses on the joint input and state estimation for linear stochastic discrete-time systems. To obtain unique estimators that are optimal in the sense of being both least-squares and minimum-variance unbiased (MVU) and their recursive solution, an objective function of the sum of squared errors of outputs is first minimized with respect to an extended state vector including states and unknown inputs. A recursive solution of the extended state vector is then derived with the aid of matrix manipulations. Finally, appropriate matrix decomposition and transformation are used to extract the recursive solutions only involving the current states and unknown inputs from the recursive solution obtained in the previous step. This approach avoids excessive computation due to the dimensions of the matrices that increase with time. As a result, the resulting recursive solution is referred to as a general Kalman filter with unknown inputs (GKF-UI), which covers the most general case of unknown inputs so far in the literature without resorting to transforming the outputs and/or unknown inputs. The unknown inputs to be estimated by the proposed GKF-UI could be arbitrary signals without any prior information and the properties of the proposed GKF-UI are also examined. A numerical example with partial feedthrough from three unknown inputs is used to demonstrate the effectiveness and accuracy of the proposed algorithm.

In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation. First, fuzzy logic systems are employed to approximate unknown nonlinear functions in the system. Next, a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states. Based on the designed adaptive fuzzy state observer, a serial-parallel estimation model is established. By applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws is developed based on Lyapunov-Krasovskii functional. It is proved that all variables of the closed-loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible. A simulation example is provided to further show the effectiveness of this novel control scheme.

This paper studies the state estimation problem of linear discrete-time systems with stochastic unknown inputs. The unknown input is a wide-sense stationary process while no other prior information needs to be known. We propose an autoregressive (AR) model based unknown input realization technique which allows us to recover the input statistics from the output data by solving an appropriate least squares problem, then fit an AR model to the recovered input statistics and construct an innovations model of the unknown inputs using the eigensystem realization algorithm (ERA). An augmented state system is constructed and the standard Kalman filter is applied for state estimation. A reduced order model (ROM) filter is also introduced to reduce the computational cost of the Kalman filter. One numerical example is given to illustrate the procedure.

In this paper, we deal with residual vector generation for fault detection problems in linear systems via unknown input observer (UIO) when the so-called observer matching condition is not satisfied. Based on the relative degree between unknown input and output, a vector of the auxiliary output is introduced so that the observer matching condition is satisfied with respect to the vector. Auxiliary outputs are related to the derivatives of measured signals. However, differentiation leads to excessive amplification of measurement noise. A dynamically equivalent configuration of linear systems is developed using successive integrations to avoid differentiation. As such, auxiliary outputs are constructed without differentiation. Then, the equivalent dynamic system and its corresponding auxiliary outputs are used to generate the residual vector via an exponentially converging UIO. Fault detection in the generated residual vector is also investigated. Finally, the effectiveness of the proposed method is shown via numerical simulation.

The robust regulator problem for linear MIMO systems in the frequency domain is considered. The stability robustness of the overall system is analysed with respect to additive perturbations in the mathematical model of the plant, and a controller that has been designed to solve the regulator problem for the nominal plant Po(s). It is shown that in the special case where the reference signal (or the disturbance) has a pole at s =jωk, the robustness can be upper-bounded by the minimum singular value of Po(jωk). This upper bound can be achieved in the case of a stable plant and step reference and disturbance. A design procedure for obtaining >H∞ -optimal solutions is given.

This paper concerns structured systems, namely linear systems where the state-space matrices have zeros in some fixed positions, and free parameters in all other entries. In particular, it focuses on discrete-time linear time-invariant systems affected by an unknown input. The goal is to study delay-L left invertibility, namely the possibility to reconstruct the input sequence from the output sequence, assuming that the initial state is known, and requiring that the inputs can be reconstructed at least up to L time steps before the current output. Under the assumption that the unknown input is scalar, this paper presents a simple graphical condition characterizing the structured systems which are generically delay-L left invertible.

In this paper, a robust state estimation problem for discrete-time systems with unknown exogenous inputs is investigated utilizing a risk-sensitive filtering approach. By proposing a Radon-Nikodym derivative, we introduce a reference measure under which the measurement and system state become independent. Based on this independent property and by treating the unknown inputs as a process modeled by a non-informative prior, we derive the reformulated risk-sensitive cost criterion under the reference measure and further propose a recursive algorithm for the risk-sensitive state estimate. A simulation example is provided to validate the theoretical results, where the proposed estimator is shown to outperform the MMSE estimator for unknown input case under the scenario subject to system parameter uncertainties.

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario. Copyright © 2016 John Wiley & Sons, Ltd.

Bond-Graph-Based Multivariable non linear UlO-type estimation

This paper is concerned with the tracking control of a class of uncertain strict-feedback systems subject to partial loss of actuator effectiveness, in addition to uncertain model dynamics and unknown disturbances. A resilient anti-disturbance dynamic surface control method is proposed to achieve stable tracking regardless of partial actuator faults. First, data-driven adaptive extended state observers are designed based on memory-based identifiers, such that the uncertain model dynamics, external disturbances and the unknown input gains due to actuator faults can be estimated. Next, a resilient anti-disturbance dynamic surface controller is developed based on recovered information from the data-driven adaptive extended state observers. After that, it is proven that the cascade system formed by the observer and controller is input-to-state stable. Finally, comparative studies are performed to validate the efficacy of the resilient anti-disturbance dynamic surface control method for nonlinear strict-feedback systems subject to partial loss of actuator effectiveness.

This paper deals with the problem of fault estimation for linear and nonlinear systems. An adaptive proportional integral observer is designed to estimate both the system state and sensor and actuator faults which can affect the system. The model of the system is first augmented in such a manner that the original sensor faults appear as actuator faults in this new model. The faults are then considered as unknown inputs and are estimated using a classical proportional-integral observer. The proposed method is first developed for linear systems and is then extended to nonlinear ones that can be represented by a Takagi-Sugeno model. In the two cases, examples of low dimensions illustrate the effectiveness of the proposed method.

Adaptive neural control for mobile manipulator systems based on adaptive state observer