Multi-input Linear Systems Research Articles

Stability-constrained model predictive control

This paper presents a new approach to guaranteeing stability of model predictive control (MPC). A stability constraint is computed and propagated forward at each stage as a constraint on the magnitude of the predicted state vector for a state-space controllable-form realization. It is shown that asymptotic stability is guaranteed for the case of constrained multi-input linear time-invariant systems under full-state measurement or with state estimation for any prediction horizon and any optimization objective function.

A simple solution to the optimal eigenvalue assignment problem

The problem of the optimal eigenvalue assignment for multi-input linear systems is considered. It is proven that for an n-order system with m independent inputs, the problem is split into the following two sequential stages. Initially, the n-m eigenvalues are assigned using an (n-m)-order system. This assignment is not constrained to satisfy optimality criteria. Next, an m-order system is used to assign the remaining m eigenvalues in such a way that linear quadratic optimal criteria are simultaneously satisfied. Therefore, the original n-order optimal eigenvalue assignment problem is reduced to an m-order optimal assignment problem. Moreover, the structure of the equivalent m-order system permits further simplifications which lead to solutions obtained by inspection.

Partially Decentralized Control of Large Scale Systems with Prescribed Stability

This paper discusses the problem of assigning the eigenvalues of a multi-input linear large scale system (LSS) in such a way that a certain degree of decentralized state feedback controls is obtained. It is proven that for an n-order system with m independent inputs the problem is split into the following two sequential stages. Initially the n-m eigenvalues are assigned using an n-m order system. This assignment determines the non-square part of the state feedback gain-matrix. Next, an m-order system is used to assign the remaining m eigenvalues so that the square part of the state feedback gain-matrix takes on a diagonal form. Therefore, the state feedback gain-matrix leads to partially decentralized control schemes since each input is fed-back by a local state variable and n-m common state variables. For LSS, this means a drastic reduction of the measured states at each input, from n to n-m+1, without any risk on stability.

A subspace algorithm for the identification of discrete time frequency domain power spectra

In this paper we present a new subspace algorithm for the identification of multi-input multi-output linear discrete time systems from measured power spectrum data. We show how the state space system matrices can be determined by taking the inverse discrete Fourier transform of the given data and applying the result to a new realization algorithm. Special attention is paid to ensure the positive realness of the identified power spectrum. The computational speed is improved by applying a Lanczos algorithm. The algorithm is illustrated with two practical examples.

Correction to "Quadratic Stabilizability Of Multi-input Linear Systems With Structural Independent Time-varying Uncertainties"

Correction to "Quadratic Stabilizability Of Multi-input Linear Systems With Structural Independent Time-varying Uncertainties"

Quadratic stabilizability of multi-input linear systems with structural independent time-varying uncertainties

This paper investigates the problem of designing a linear-state feedback control to stabilize a class of multi-input linear dynamical systems. We first show that to ensure a stabilizable system, some entries of the system matrices must be sign-invariant. We then derive a sufficient condition under which a system can he quadratically stabilized by a linear control.

Solvability conditions for disturbance decoupling problems with static measurement feedback

Two well-known disturbance decoupling problems are considered. A checkable necessary and sufficient condition is derived under which the disturbance decoupling problem with static measurement feedback (DDPKM) is solvable for a class of multi-input and multi-output linear time-invariant systems, which have a left invertible transfer matrix function from the control input to the controlled output. The set of all solutions that solve the DDPKM is constructed and parametrized explicitly. This set is then used to solve the disturbance decoupling problem with static measurement feedback and with internal stability (DDPKMS).

A Robust Disturbance Observer for Uncertain Linear Systmes

When modeling error is large of plant is time-varying, it is hard to obtain good robust performance and robust stability by conventional contorl methods. Here, we need to design a robust controller bearing modeling error. In this paper, based on recently developed Time Delay Control(TDC) and Disturbance Observer the output feedback Robust Disturbance Observer(RDO), which is easily combined with general linear control, is proposed. Proposed RDO is derived from extending the main idea of Disturbance Observer to multi-input multi-output linear system. RDO solves robust stability problem of Disturbance Observer and has the robust performance same as nominal performance. RDO controlled dual stage positioning system shows excellent robust performance.

Algorithm 747: a Fortran subroutine to solve the eigenvalue assignment problem for multiinput systems using state feedback

The implementation of an algorithm for the computation of a state feedback for multiinput linear systems, resulting in a closed-loop matrix with a specified self-conjugate set of eigenvalues, is presented. The computation uses only real arithmetic, assigning complex conjugate eigenvalues in one double step. The implementation uses level-1 BLAS routines where possible. A brief description of the algorithm is also given.

Response function estimation from multi-input systems

In this work a novel formalism to estimate the vector linear impulse response functions from the experimental data observed from a multi-input system, allowing for correlation between the inputs, is developed. Time series statistical moments are estimated from the data and are used as the basis of a set of simultaneous equations in the unknown response functions. These simultaneous equations are solved using standard matrix methods for the unknown linear response functions. This approach is an extension to one proposed by Box and Jenkins from the Yule-Walker equations. The ability of the technique to correctly estimate the response functions of a multi-input linear system to a high degree of accuracy is demonstrated, using a numerical example where the properties of the system are known and there is strong correlation between the input data. This novel technique is then used to estimate the response functions of the coupled convective and radiative processes, that act at the internal surface of the ceiling of an experimental building. The area under the estimated response function of each process is the gain or heat transfer coefficient for that process. The estimated response functions from a multi-input analysis are compared with those obtained from a set of analyses where each input is treated as being independant of the others. The response functions, of each process, estimated by the two approaches (single- and multi-input) were employed to predict an out-of-sample period of the surface heat flux, given the convective and radiative driving forces, which could be compared with the measured heat flux. The differences between the results obtained from the two approaches are explained by considering the correlation between the driving forces of the convective and radiative processes.

Minimum Energy Control for Multi-Input Linear Digital Systems in z-Domain.

Minimum Energy Control for Multi-Input Linear Digital Systems in z-Domain.

Semiglobal stabilization of multi-input linear systems with saturated linear state feedback

For multi-input linear systems with eigenvalues in the closed left-half comlex plane, we address the problem of stabilization by a linear state feedback subject to saturation. Using an eigenvalue-generalized eigenvector assignment technique, we prove that such systems can be semiglobally stabilized with a saturated linear state feedback. Based on this result, we propose an algorithm to calculate an ε-parametrized family of state feedback gain matrices that semiglobally stabilize the system. Two examples are used to illustrate the results.

CONDITIONAL SIMULATION OF SPACE-TIME VARIATION OF EARTHQUAKE GROUND MOTION BY USING MULTI-INPUT LINEAR SYSTEMS THEORY

CONDITIONAL SIMULATION OF SPACE-TIME VARIATION OF EARTHQUAKE GROUND MOTION BY USING MULTI-INPUT LINEAR SYSTEMS THEORY

Closed-Loop Expression of Fixed-end-point LQ Optimal Control for Digital Systems

This paper discusses the fixed-end-point linear-quadratic optimal control problem for a multi-input linear time-invariant discrete-time system. Using the general form of the inputs which satisfy the zero-end-point condition, the fixed-end-point problem is transformed into the new free-end-point problem and the special deadbeat control. The optimal inputs are made up of three phases, and they are expressed by the variable gain state feedback and the special deadbeat control. The variable gains are obtained by the special nonstationary Riccati equations, and all gains do not depend on the initial state.

New Optimality Condition of Fixed-End-Point Regulator for Multi-Input Linear Digital Systems

This paper discusses the regulator problem with the zero terminal state for a multi-input linear digital system. First, for a general additive performance index, the fundamental structure of the regulator which drives the state to zero within a finite time is obtained. This problem is divided into three phases : the new free-end-point problem in the first phase, the new free-end-point problem for the new time-variant system with the time-variant structure of the new inputs in the second phase, and the constant gain special deadbeat control in the third phase. That is, the new optimality condition of the fixed-end-point regulator is expressed by the special deadbeat control and the optimality condition of the induced free-end-point regulator. Furthermore, the closed-loop expression for the quadratic performance index is obtained to show the effectiveness of the new optimality condition.

State feedback design using reduced-order nonsquare descriptions

A pole-placement technique is proposed for computing state feedback in multi-input linear systems. The algorithm has good numerical behavior and utilizes nonsquare pencils and the notion of decomposability. The fact that the method deals with reduced-order pencils and exploits the Schur-Hessenberg form improves the conditioning of the problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New Condition of Optimality for Multi-Input Linear Digital Regulator with Fixed Terminal State.

This paper discusses the regulator problem with the fixed terminal state for multi-input linear digital systems. First, for the general additive performance index, the fundamental structure of the regulator which drives the state to zero within a finite time is obtained. This problem is divided into three phases: the new free terminal state problem in the first phase, the new free terminal state problem for the time-variant system with the time-variant structure of the new input in the second phase, and the constant gain special deadbeat control in the third phase. That is, the new condition of optimality of the regulator problem with the fixed terminal state is expressed by the special deadbeat control and the induced regulator problem with the free new terminal state. The new solution of the deadbeat linear-quadratic optimal control problem is obtained to show the effectiveness of the new condition of optimality

A new control design for multiterminal HVDC systems using optimal entire eigenstructure assignment

This paper presents a new method of control design for multiterminal HVDC systems. The proposed design approach applies the optimal entire eignestructure assignment technique developed for optimal state feedback controls of multi-input linear systems in order to achieve predetermined response characteristics. The feedback-gains are computed to assign the closed-loop eigenvalues of the HVDC system at any specified distinct modes and simultaneously minimize an appropriate linear quadratic (LQ) performance index. Therefore, the controller design takes into account the dynamics of the DC transmission system, making possible the regulation of the current at the remote terminals, and at the same time assures both stability with predetermined duration of transient response and minimum system effort. A computer simulation of an integrated ac/dc power system is used to demonstrate the effectiveness of the proposed design since in all simulated cases the transient response for typical disturbances appears desirable, showing fast damping characteristics without significant overshoots or oscillations.

Minimization of the input energy of regulator problems with the fixed terminal state. The case of multi-input linear time-invariant discrete-time systems.

This paper discusses the regulator problem of minimizing the input energy for the multi-input linear time-invariant discrete-time system with the zero terminal state. The performance index is the sum of the quadratic forms of the input vectors. By using the deadbeat principle, the system is transformed into the new time-variant system with the time-variant structure of the new input. The performance index is transformed into the sum of the quadratic forms of the new state vectors and the new input vectors with cross terms, and the new terminal state is free. The optimal inputs are given by the variable gain state feedback in the first phase, by linear combinations of the constant gain state feedback and the variable gain state feedback in the second phase, and by the constant gain state feedback in the third phase. The variable gains are obtained by using the special Riccati equation. Both gains are independent of the initial state.

Feedback controls for pole subset assignment

A pole assignment problem for multi-input linear systems is discussed. In conventional pole assignment problems, an input is concerned with all poles simultaneously or it assigns only a specified subset of poles. Here we propose a design method which makes each input assign an arbitrary subset of poles. Thus when we replace a pole by using this method, it is enough to reconstruct only the corresponding input.