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The design and analysis of active disturbance rejection control (ADRC) is considered for a globally Lipschitz nonlinear discrete-time system which is nonaffine to control inputs. A local dynamic linearization (LDL) is proposed to transfer the original nonaffined nonlinear system into a nonlinear system affine to control input such that the open problem of selecting a control gain in the feedback control law of ADRC is solved. Further, both a parameter updating law and an adaptive extended state observer are designed to estimate control gains and total uncertainty, respectively. The stability of ADRC for nonlinear nonaffine discrete-time processes is analyzed rigorously for the first time with the aid of contraction mapping principle. The proposed adaptive feedback controller considers desired reference trajectory, parameter adaption, error feedback and the compensation of total uncertainties caused by parameter estimation error and unknown nonlinearity simultaneously to achieve better control performance. The proposed method is nearly data driven since no other model information is needed except for the globally Lipschitz condition and the nonzero property of the partial derivative of the nonlinear system with respect to the control input. The theoretical result is verified by simulations.

This article investigates a challenging open problem of convergence analysis of sampled-data iterative learning control for locally Lipschitz continuous (LLC) nonlinear nonaffine continuous-time systems. The restrictive repetitive conditions are relaxed by taking the LLC nonlinear nonaffine systems with iteratively variant initial states, reference trajectories, and exogenous disturbances into consideration. A new convergence analysis method is proposed by incorporating the mathematical induction with the contraction mapping principle (MI-CMP) to prove the boundedness of system variables, and bounded convergence of tracking error for a finite iteration as the first step. Then, the mathematical proof by contradiction is utilized along with the MI-CMP to further prove the robust convergence of the tracking error in any iteration to an error bound related to the bounds of the iteration-varying uncertainties and the sampling period. It is also shown that the tracking error converges to a smaller bound if the iteration-varying uncertainties disappear, even to zero if the sampling period approaches zero. In addition, an algorithm is provided to optimize the learning operator under the convergence condition. Theoretical results are further verified by simulations.

In this paper, we propose a new approach to state estimation of multiple state-space models. Unlike the traditional methods (including the interacting multiple-model algorithm) that approximate a Gaussian mixture distribution with a single Gaussian distribution, the proposed method approximates the joint probability density functions of the state and model identity through Bayesian inference. It is shown that the proposed method reduces the approximation error considerably, and improves estimation accuracy without increasing computational cost. Analysis of its specific features as well as a potential extension is also presented. Numerical examples with a practically oriented simulation are employed to illustrate the effectiveness of the proposed method.

In this paper, an iterative residual generator (IRG) is proposed for discrete time-invariant state–space model with the aim of detecting faulty signals. By minimizing the mean square errors subject to unbiasedness constraint, a new filter with finite impulse response structure is derived. The resulting IRG is then obtained by extracting residual signal from the batch filter through several predictor/corrector iterations. It shows that IRG can provide a zero-mean Gaussian process regardless of previous estimation errors. More importantly, it includes the residual generation process in the Kalman filter as its special case. With the chi-square test, a numerical example is simulated to demonstrate that IRG can reduce the false alarm significantly compared with the traditional recursive strategy in the presence of actuator or sensor faults, and the estimation horizon length in IRG serves as a tuning parameter providing a tradeoff between the missed alarm and false alarm.

In this technical note, an optimal unbiased filter (OUF) is derived for time-variant systems to relax the initial condition assumption in Kalman filter (KF). By minimizing the mean square errors subject to the unbiasedness condition a solution is derived in a batch computation form first. To facilitate the on-line application, a recursive realization is further developed. The effect of removing the initial condition assumption on the estimation performance is analysed, and we show that the proposed algorithm converges to the KF asymptotically. Two-state harmonic model and four-state moving target tracking model are employed to demonstrate that the OUF can improve transient estimation performance significantly and can be used in place of the KF when the apriori information about the initial state values is not available.

We consider the stabilization problem for a class of networked control systems in the discrete-time domain with random delays. The sensor-to-controller and controller-to-actuator delays are modeled as two Markov chains, and the resulting closed-loop systems are jump linear systems with two modes. The necessary and sufficient conditions on the existence of stabilizing controllers are established. It is shown that state-feedback gains are mode-dependent. An iterative linear matrix inequality (LMI) approach is employed to calculate the state-feedback gains.

This note is concerned with model predictive control for linear singular systems with time-varying uncertainties. A piecewise constant control sequence is calculated by minimizing the worst-case linear quadratic objective function. At each sample time, the sufficient conditions on the existence of the model predictive control are derived and expressed as linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method.

Actuator saturation constraint is inevitable in industrial process. In this note, we consider a discrete receding horizon control, a piecewise constant robust model predictive control, for a continuous-time plant with actuator saturation constraint through a sampled-data control approach. The solution is formulated as an optimization problem subject to linear matrix inequalities. A numerical example is used to demonstrate the effectiveness of the proposed design procedure.

This book is timely as a state-of-the-art summary on some of the most recent developments in control loop performance assessment. In reality, the book provides a broader context to control performance assessment other than merely evaluating the controller performance. What is also discussed includes business performance benchmarking, economic auditing of control systems, plantwide disturbance diagnosis, oscillation detection, and valve stiction monitoring, As such, this book covers topics beyond traditional control loop performance assessment. Overall, the book is well written. An excellent feature is that detailed step-by-step procedures for algorithm implementation are given, which can be a good user's guide. Extensive simulation and industrial examples are cited to illustrate the algorithms. The book provides a food balance between academic and engineering aspects. Academic researchers, graduate students, and industrial practitioners who are interested in the general areas of control performance monitoring, business performance benchmarking, control system or instrument problem diagnosis will find this book a useful reference.

The commenters point out a major problem with the initialization stage in the technique in the above article by Casavola et al. (see ibid. vol. 47, no. 7, p. 1147-53, 2002)