Constrained Linear Systems Research Articles

On the dynamic improvement in linear constrained control discrete-time systems

In the control of linear systems with asymmetrical input constraints, larger domains of initial states can be obtained by allowing slow initial dynamics of the system in a closed loop, and making it faster during its evolution. The positive invariance concept application leads to piecewise linear constrained control laws using asymmetrical polyhedral sets.

Robust pole assignment in complex plane regions for linear uncertain constrained control systems

A new design for pole assignment in complex plane regions is presented. Vectorial bounds for structured uncertainties such that the assigned poles remain in these regions are given. Application to the linear constrained regulator problem is achieved. This approach makes a link between the pole assignment procedure used for constrained control and sufficient conditions established to check the positions of eigenvalues in the complex plane for a given matrix.

Convergence of constrained model-based predictive control for batch processes

The convergence property of constrained model-based predictive control for batch processes (BMPC) is investigated. BMPC is a recently developed control technique that combines iterative learning control with real-time predictive control. It is proven for a general class of linear constrained systems that the tracking error converges to zero as the run number increases.

Semi-Ellipsoidal Controlled Invariant Sets for Constrained Linear Systems

This paper investigates an alternative approximation to the maximal viability set for linear systems with constrained states and input. Current ellipsoidal and polyhedral approximations are either too conservative or too complex for many applications. As the primary contribution, it is shown that the intersection of a controlled invariant ellipsoid and a set of state constraints (referred to as a semi-ellipsoidal set) is itself controlled invariant under certain conditions. The proposed semi-ellipsoidal approach is less conservative than the ellipsoidal method but simpler than the polyhedral method. Two examples serve as proof-of-concept of the approach.

Model-based iterative learning control with a quadratic criterion for time-varying linear systems

In this paper, iterative learning control (ILC) based on a quadratic performance criterion is revisited and generalized for time-varying linear constrained systems with deterministic, stochastic disturbances and noises. The main intended area of application for this generalized method is chemical process control, where excessive input movements are undesirable and many process variables are subject to hard constraints. It is shown that, within the framework of the quadratic-criterion-based ILC (Q-ILC), various practical issues such as constraints, disturbances, measurement noises, and model errors can be considered in a rigorous and systematic manner. Algorithms for the deterministic case, the stochastic case, and the case with bounded parameter uncertainties are developed and relevant properties such as the asymptotic convergence are established under some mild assumptions. Numerical examples are provided to demonstrate the performance of the proposed algorithms.

Any Domain of Attraction for a Linear Constrained System is a Tracking Domain of Attraction

In the stabilization problem for systems with control and state constraints a domain of attraction is a set of initial states that can be driven to the origin by a feedback control without incurring constraints violations. If the problem is that of tracking a reference signal, that converges to a constant constraint-admissible value, a tracking domain of attraction is a set of initial states from which the reference signal can be asymptotically approached without constraints violation during the transient. Clearly, since the zero signal is an admissible reference signal, any tracking domain of attraction is a domain of attraction. We show that the opposite is also true. For constant reference signals we establish a connection between the convergence speed of the stabilization problem and tracking convergence which turns out to be independent of the reference signal. We also show that the tracking controller can be inferred from the stabilizing (possibly nonlinear) controller associated with the domain of attraction.

Reducing on-line computational demands in model predictive control by approximating QP constraints

Abstract In this paper, we propose two Model Predictive Control algorithms, whose on-line computational demands are significantly smaller than that for conventional Model Predictive Control algorithms, for control of large-scale constrained linear systems. We show that closed-loop stability can be guaranteed under some conditions. We also propose an optimal anti-windup scheme for approximating Model Predictive Control (thus eliminating the need for solving an on-line optimization problem) and derive a quantitative condition under which Model Predictive Control can be approximated effectively. These results make Model Predictive Control a very attractive candidate to be applied to systems with small sampling times and/or with a large number of inputs, and address achievable constrained performance by any anti-windup design.

Adaptive Stabilization and Tracking of Constrained Linear Systems

We are considering the problem of controlling partially known linear plants submitted to a control saturation constraint. We seek both plant global stabilization and output tracking. We propose a direct pole-placement adaptive controller and show that if the closed loop poles are placed in a specific region then the desired stability and tracking objectives are achieved.

A Robust Model Predictive Control Scheme for Constrained Linear Systems

This paper presents a novel model predictive control scheme for stable and unstable, linear, discrete time, multi-variable processes, for which robust stability of the closed-loop system is proven. The uncertainty description considered is related to the well-tried M — Δ structure that is popular for many robust controller design techniques including H∞ methods. Here, the uncertainty description is extended to also cover parametric uncertainties and a class of nonlinear uncertainties. The resulting MPC controller requires the on-line solution of a computationally attractive convex minimax optimization problem.

An Optimal Design of Constrained Linear Control Systems Using the Set of Admissible Gains

In the design problem of linear control systems with input and state constraints, a feedback gain is admissible if all the constraints are satisfied. This paper presents a new design method for obtaining a suboptimal linear admissible control law using a criterion for admissible gain when the set of initial states is given by a convex polyhedron. A function of gain on the constrained conditions, α(f), is defined so that a. stable gain f is admissible α(f)≤1. An effective method for computing α(f) by means of an LP algorithm is proposed, which is based on the method of constructing the maximal set of admissihle initial states in the dual space.

Comment On “Unit Graph Estimation and Stabilization Using Quadratic Programming and Difference Norms” By C. R. Dietrich and T. G. Chapman

Water Resources ResearchVolume 31, Issue 10 p. 2633-2634 CommentariesFree Access Comment On “Unit Graph Estimation and Stabilization Using Quadratic Programming and Difference Norms” By C. R. Dietrich and T. G. Chapman C. Nagaraju Kumar, C. Nagaraju KumarSearch for more papers by this authorK. Elango, K. ElangoSearch for more papers by this author C. Nagaraju Kumar, C. Nagaraju KumarSearch for more papers by this authorK. Elango, K. ElangoSearch for more papers by this author First published: October 1995 https://doi.org/10.1029/95WR00892AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. References Bras, R. L., I. Rodriguez-Iturbe, Random Functions and Hydrology, Addison-Wesley, Reading, Mass., 1985. Bree, T., The stability of parameter estimation in the general linear model, J. Hydrol., 37, 47– 66, 1978. Dietrich, C. R., T. G. Chapman, Unit graph estimation and stabilization using quadratic programming and difference norms, Water Resour. Res., 298, 2629– 2635, 1993. Kandasamy, L. C., E. J. James, C. Nagaraju Kumar, H. Suresh Rao, K. Elango, Rainfall-runoff modelling of mountainous river basins55th Research and Development Session, Technical Session IICent. Board of Irrig. and PowerSrinagar, India, 1989. Martelli, S., E. Todini, J. R. Wallis, CLS: Constrained linear systems, Mathematical Models for Surface Water Hydrology T. A. Ciriani, U. Maione, J. R. Wallis, 295– 329, John Wiley, New York, 1977. Nagaraju Kumar, C., Falling limb criterion for optimising basin response function, M. Tech. thesis,Dep. of Civ. Eng., Indian Inst. of Technol.,Madras,June1988. Singh, P. K., Unit hydrographs-A comparative study, Water Resour. Bull., 122, 381– 391, 1976. Todini, E., J. R. Wallis, Using CLS for daily or longer period rainfall-runoff modelling, Mathematical Models for Surface Water Hydrology T. A. Ciriani, U. Maione, J. R. Wallis, 149– 168, John Wiley, New York, 1977. Volume31, Issue10October 1995Pages 2633-2634 ReferencesRelatedInformation

Least Controls for a Class of Constrained Linear Stochastic Systems

This paper introduces a class of constrained linear stochastic systems. The main objective is to investigate whether there exists a least control, in a sense that it exerts least effort in controlling the system to within a predetermined region. Our approach of finding a least control is: (a) to characterize a class of functional polyhedral sets of functions which have least elements, and (b) to construct a least-control process through these least elements. Existence of a least control is established. And the connection between a least control and a solution of the dynamic complementarity problem (DCP) is also discussed.

Computation of state realizations for control systems described by a class of linear differential-algebraic equations

Control systems described in terms of a class of linear differential-algebraic equations are introduced. Under appropriate relative degree assumptions, a computational procedure for obtaining an equivalent state realization is developed using a singular value decomposition. Properties such as stability, controllability, observability, etc, for the differential-algebraic system may be studied directly from the state realization. For linear constrained hamiltonian systems, it is shown that the procedure provides a state realization in which the hamiltonian structure is preserved. Similar results are obtained for constrained gradient systems. Control of systems described by this class of differential-algebraic equations, using a transformation to obtain a state realization, completely avoids the need for any new control theoretic machinery.

Reachability in input constrained discrete-time linear systems

A complete picture of dynamic system theory and optimization should include the study of linear constrained systems. Surprising little work has been done so far in this area. In this paper a rather complete theory of linear discrete time systems with general constraints on the input is developed. It covers reachability theory and gives also the discrete time version of the bang-bang principle for convex constraints.

Invariant Regulators for a Class of Constrained Linear Systems

Stable dynamic systems admit positively invariant domains associated to their Lyapunov functions. Conversely, some domains can be made positively invariant for systems with state feedback controllers designed in such a way that some associated definite non-negative functions are bound to decrease. In particular, this approach can be used to establish conditions on the gain matrix for Linear Constrained Regulation Problems (LCRP). We propose a fixed and a variable regulator easy to compute through linear programming, for a class of contrained linear systems

Robust stabilization of linear constrained uncertain time delay systems

The sufficient conditions for the robust stability of constrained uncertain time delay systems are presented in the time domain. The properties of the matrix measure and comparison theorem are used in the formulation. Then, a method is proposed for the design of a robust state feedback controller to satisfy the robustness requirement. Examples are given to illustrate the proposed method.

A nonlinear time-variant constrained model for rainfall-runoff

Models of the rainfall-runoff process can be segregated into two classes: those based on input-output (black box) techniques, and those based, directly or indirectly, on the laws of physics. Both approaches have limitations and advantages. In this paper a combined model is described which incorporates an approximate description of the physical process to estimate effective precipitation and uses the input-output estimation procedure of the constrained linear system (CLS) model to relate effective precipitation to runoff. Results are presented which demonstrate that certain problems of poor calibration and prediction encountered with the CLS model are significantly reduced by using estimated effective precipitation in place of actual precipitation. Use of the precipitation preprocessor with the CLS runoff model effectively incorporates nonlinear and time-variant dynamics without the necessity for multiple-parameter vectors and antecedent precipitation thresholds required by the original version of CLS. Additional refinements, including time variability of some of the parameters, can easily be accommodated in the new formulation.

Using a Desk-Top Computer for an On-Line Flood Warning System

The paper deals with the development of an adaptive model that is applicable to real-time forecasting of hydrologic processes. The rainfall-runoff process is considered here. In this model the discharge was modeled as autoregressive with past discharges and a moving average representation on the precipitation. The model makes use of the Constrained Linear Systems (CLS) technique to split the precipitation into two rainfall inputs by using a threshold based on an antecedent precipitation index. This technique can be thought of as a piecewise linearization of a nonlinear process. The real-time forecasting model is a time invariant linear state model where the state variables, discharge and rainfall, are estimated by the Kalman filtering algorithm and the unknown model parameters by using the instrumental variables approach. This technique was applied in a case study using data from the Ombrone River Basin, Italy, and was implemented on a small desk-top computer.