Model falsification using set‐valued observers for a class of discrete‐time dynamic systems: a coprime factorization approach

This article introduces a new method for model falsification using set‐valued observers, which can be applied to a class of discrete linear time‐invariant dynamic systems with time‐varying model uncertainties. In comparison with previous results, the main advantages of this approach are as follows: The computation of the convex hull of the set‐valued estimates of the state can be avoided under certain circumstances; to guarantee convergence of the set‐valued estimates of the state, the required number of previous steps is at most as large as the number of states of the nominal plant; and it provides a straightforward nonconservative method to falsify uncertain models of dynamic systems, including open‐loop unstable plants. The results obtained are illustrated in simulation, emphasizing the advantages and shortcomings of the suggested method. Copyright © 2013 John Wiley & Sons, Ltd.     

Some properties of the dual adaptive stochastic control algorithm

The purpose of this paper is to compare analytically the properties of the suboptimal dual adaptive stochastic control with those of the optimal control, when plant dynamic contain multiplicative white noise parameters. A simple scalar example is used for this analysis.     

Suboptimal state estimation for continuous-time nonlinear systems from discrete noisy measurements

This paper presents the derivation of the dynamical equations of a second-order filter which estimates the states of a non-linear plant on the basis of discrete noisy measurements. The filter equations contain terms involving the second-order partial derivatives of the plant and output equations. Simulation results are presented which yield a comparison of the performance of the first-versus the second-order filter when applied to a nonlinear third-order system. The results indicate that the inclusion of second-order terms can markedly improve the filter performance.     

On the design of optimal constrained dynamic compensators for linear constant systems

The design of linear time-invariant dynamic compensators of fixed dimensionalitys, which are to be used for the regulation of annth-order linear time-invariant plant, is dealt with. A modified quadratic cost criterion is employed in which a quadratic penalty on the system state as well as all compensator gains is used; the effects of the initial state are averaged out. The optimal compensator gains are specified by a set of simultaneous nonlinear matrix algebraic equations. The numerical solution of these equations would specify the gain matrices of the dynamic compensator. The proposed method may prove useful in the design of low-orderscompensators for high-ordernplants that have fewroutputs, so that the dimension of the compensator is less than that obtained through the use of the associated Kalman-Bucy filternor the Luenberger observern - r.     

Adaptive stochastic control for a class of linear systems

The problem considered in this paper deals with the control of linear discrete-time stochastic systems with unknown (possibly time-varying and random) gain parameters. The philosophy of control is based on the use of an open-loop feedback optimal (OLFO) control using a quadratic index of performance. It is shown that the OLFO system consists of 1) an identifier that estimates the system state variables and gain parameters and 2) a controller described by an "adaptive" gain and correction term. Several qualitative properties and asymptotic properties of the OLFO adaptive system are discussed. Simulation results dealing with the control of stable and unstable third-order plants are presented. The key quantitative result is the precise variation of the control system adaptive gains as a function of the future expected uncertainty of the parameters; thus, in this problem the ordinary "separation theorem" does not hold.     

Conic sectors for sampled-data feedback systems

A multivariable analog system can be controlled by a sampled-data compensator. A conic sector that can be used to analyze the closed-loop stability and robustness of this feedback system is presented in this letter.     

The LQG/LTR procedure for multivariable feedback control design

This paper provides a tutorial overview of the LQG/LTR design procedure for linear multivariable feedback systems. LQG/LTR is interpreted as the solution of a specific weighted H²-tradeoff between transfer functions in the frequency domain. Properties of this solution are examined for both minimum-phase and nonminimum-phase systems. This leads to a formal weight augmentation procedure for the minimum-phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights. While such arbitrary specifications are not possible for nonminimum-phase problems, a direct relationship between weights and sensitivities is developed for nonminimum-phase SISO and certain nonminimum-phase MIMO cases which guides the weight selection process.     

Stability‐ and performance‐robustness tradeoffs: MIMO mixed‐µ vs complex‐µ design

We present a non‐trivial case study designed to highlight some of the practical issues that arise when using mixed‐µ or complex‐µ robust synthesis methodologies. By considering a multi‐input multi‐output three‐cart mass–spring–dashpot (MSD) with uncertain parameters and dynamics, it is demonstrated that optimized performance (disturbance‐rejection) is reduced as the level of uncertainty in one or two real parameters is increased. Comparisons are made (a) in the frequency domain, (b) by RMS values of key signals and (c) in time‐domain simulations. The mixed‐µ controllers designed are shown to yield superior performance as compared with the classical complex‐µ design. The singular value decomposition analysis shows the directionality changes resulting from different uncertainty levels and from the use of different frequency weights. The nominal and marginal stability regions of the closed‐loop system are studied and discussed, illustrating how stability margins can be extended at the cost of reducing performance. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of gain scheduled control for nonlinear plants

Gain scheduling has proven to be a successful design methodology in many engineering applications. In the absence of a sound theoretical analysis, these designs come with no guarantees of the robustness, performance, or even nominal stability of the overall gain-scheduled design. An analysis is presented for two types of nonlinear gain-scheduled control systems: (1) scheduling on a reference trajectory, and (2) scheduling on the plant output. Conditions which guarantee stability, robustness, and performance properties of the global gain schedule designs are given. These conditions confirm and formalize popular notions regarding gain scheduled designs, such as that the scheduling variable should vary slowly, and capture the plant's nonlinearities