Output tracking control of a parallel-flow heat exchange process

In this paper, we consider an output tracking problem of a parallel-flow heat exchange process with distributed and boundary inputs. As the distributed inputs to the system, the output feedback control is first applied. Under zero boundary inputs, it is shown that the C₀-semigroup describing the closed-loop system satisfies the spectrum determined growth condition. Next, we apply a backstepping method to the design of the boundary inputs for output tracking. Our main result shows that the output of the system reaches a reference signal in finite time under both the output feedback control and the boundary control law derived by the backstepping method.     

H∞ sampled-data synthesis and related numerical issues

In this paper we present a new, compact derivation of state-space formulae for the so-called discretisation-based solution of the H_∞ sampled-data control problem. Our approach is based on the established technique of continuous time-lifting, which is used to isometrically map the continuous-time, linear, periodically time-varying, sampled-data problem to a discretetime, linear, time-invariant problem. State-space formulae are derived for the equivalent, discrete-time problem by solving a set of two-point, boundary-value problems. The formulae accommodate a direct feed-through term from the disturbance inputs to the controlled outputs of the original plant and are simple, requiring the computation of only a single matrix exponential. It is also shown that the resultant formulae can be easily re-structured to give a numerically robust algorithm for computing the state-space matrices.     

Robust output-feedback control of linear discrete-time systems

The problem of designing H_∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H_∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.     

Adaptive H_∞ Control for Nonlinear Hamiltonian Systems with Time Delay and Parametric Uncertainties

This paper addresses the adaptive H∞ control problem for a class of nonlinear Hamiltonian systems with time delay and parametric uncertainties. The uncertainties under consideration are some small parameter perturbations involved in the structure of the Hamiltonian system. Both delay-independent and delay-dependent criteria are established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii functional approach. In order to construct the adaptive H∞controller, the situation that the parameter perturbation is inexistent in the system is also studied and the controller is designed.The adaptive H∞ control problem is solved under some sufficient conditions which ensure the asymptotic stability and the L2 gain performance of the resulted closed-loop system. Numerical example is given to illustrate the applicability of the theoretical results.     

Flow regularity and optimality conditions with controls inL p

In this paper we study theC ^p regularity of the flow of a nonlinear nonautonomous control system with respect to control maps belonging toL ^p withp≥r. The results obtained are applied to get first- and second-order optimality conditions when the control space isL ^p . The problem which we consider is in the Mayer form and includes endpoint constraints. We present first-order necessary conditions for a wide class of control systems. Moreover, we show that the usual second-order sufficient conditions are effective only if the mapf that defines the control system is a polynomial of degree two in the control variable and the controls belong toL ².     

Leader–follower synchronisation of autonomous agents with external disturbances

The synchronisation problem is investigated for multiple linear agents with external disturbances that are guided by a leader with different dynamics. A method is presented for designing a networked controller that synchronises the agents. First, a general dynamic controller with two inputs is proposed that introduces the model of the leader as an internal reference model into the control loop of all the following agents. Second, the two inputs to the local controllers of the followers are designed by H_∞ control theory such that the resulting closed-loop system achieves the output synchronisation with a desired disturbance attenuation performance. The proposed method is applied to the leader–follower synchronisation of vehicles in a platoon.     

State-feedback control of systems with multiplicative noise via linear matrix inequalities

We consider LTI systems perturbed by parametric uncertainties, modeled as white noise disturbances. We show how to maximize, via state-feedback control, the smallest norm of the noise intensity vector producing instability in the mean square sense, using convex optimization over linear matrix inequalities. We also show how to maximize performance robustness, where performance is measured by expected output energy, with either bounded initial conditions and zero inputs (classical LQG cost), or zero initial conditions and deterministic inputs of bounded energy (a generalization of the H_∞ norm).     

H∞ control design in bilinear systems: a tensor formal series approach

In this paper, the H_∞ disturbance attenuation problem of bilinear system is discussed. Dynamic game theory is used to solve this bilinear minimax problem. The solvability of H_∞ disturbance attenuation in bilinear system is also discussed. The techniques of tensor products and formal power series are employed to solve the nonlinear Bellman-Isaac differential equation. Furthermore, the convergence for the tensor formal series approach of this H_∞ control problem is discussed, and the radius of convergence for this H_∞ control to be well defined is also obtained.     

Relating H2 and H∞ bounds for finite-dimensional systems

For a linear time invariant system, the infinity-norm of the transfer function can be used as a measure of the gain of the system. This notion of system gain is ideally suited to the frequency domain design techniques such as H_∞ optimal control. Another measure of the gain of a system is the H₂ norm, which is often associated with the LQG optimal control problem. The only known connection between these two norms is that, for discrete time transfer functions, the H₂ norm is bounded by the H_∞ norm. It is shown in this paper that, given precise or certain partial knowledge of the poles of the transfer function, it is possible to obtain an upper bound of the H_∞ norm as a function of the H₂ norm, both in the continuous and discrete time cases. It is also shown that, in continuous time, the H₂ norm can be bounded by a function of the H_∞ norm and the bandwidth of the system.     

Feedback stabilization of a class of distributed parameter systems with control constraints

The feedback stabilization problem for a class of infinite-dimensional linear systems with control constraints is investigated. The approach is developed using a state space system framework which is based on a semigroup formulation. In contrast to the previous works in this direction, it is not assumed that the C₀ semigroup we deal with is a semigroup of contractions. The main result links the problem with the positive invariance of appropriate polyhedral sets. Verifiable necessary and sufficient conditions for this latter property are stated.     

Delay-dependent robust stabilization and H ∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.     

Global L2-gain design for a class of nonlinear systems

It is known that the so-called H_∞ control problem of a nonlinear system is locally solvable if the corresponding problem for the linearized system can be solved by linear feedback. In this paper we prove that this condition suffices to solve also a globalH_∞ control problem, for a fairly large class of nonlinear systems, if one is free to choose a state-dependent weight of the control input. Using a two-way (backward and forward) recursive induction argument, we simultaneously construct, starting from a solution of the Riccati algebraic equation, a global solution of the Hamilton–Jacobi–Isaacs partial differential equation arising in the nonlinear H_∞ control, as well as a state feedback control law that achieves global disturbance attenuation with internal stability for the nonlinear systems.     

A Class of Functions from P 2

A number of essential properties of a class G of Boolean functions are investigated; these functions are realized by functional elements that have one output and check tests of length two that detect single constant errors at inputs and outputs of these elements. The problem of completeness of this class and questions of its relation to closed base classes in P ₂ are considered. A lower estimate of the number of all the functions of n variables from this class is obtained.     

Static output feedback stabilisation with H∞ performance for a class of plants

In this paper, the problem of static output feedback control of a linear system is considered. The existence of a static output feedback control law is given in terms of the solvability of two coupled Lyapunov inequalities which result in a non-linear optimisation problem. However, using state-coordinate and congruence transformations and by imposing a block-diagonal structure on the Lyapunov matrix, we will see that the determination of a static output feedback gain reduces, for a specific class of plants, to finding the solution of a system of linear matrix inequalities. The class of plants considered is those which are minimum phase with a full row rank Markov parameter. The method is extended to incorporate H_∞ performance objectives. This results in a sub-optimal static H_∞ control law found by non-iterative means. The simplicity of the method is demonstrated by a numerical example.     

Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

This paper¹ considers a single product and a single stocking location production/inventory control problem given a non-stationary stochastic demand. Under a widely-used control policy for this type of inventory system, the objective is to find the optimal number of replenishments, their timings and their respective order-up-to-levels that meet customer demands to a required service level. We extend a known CP approach for this problem using three cost-based filtering methods. Our approach can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all. This work was supported by Science Foundation Ireland under Grant No. 03/CE3/I405 as part of the Centre for Telecommunications Value-Chain-Driven Research (CTVR) and Grant No. 00/PI.1/C075. ¹This paper is an extended version of [19].     

Signal restoration in linear systems with trends

For the unique solution of the problem of calculation of the inputs and outputs of a linear system from observations comprising additive quasipolynomial additives (trends) with unknown parameters, the existence conditions were established. Formulas to calculate the system signals and trends from the observations of the total signal were presented.     

Persistent inputs and the standard H 2 multivariable control problem

The H ₂ control problem is formulated with exogenous inputs having unstable shape-deterministic components. Such inputs are called persistent. Some issues in connection with past solutions of the H ₂ control problem in this case are carefully described and addressed. In particular, it is established that two- and three-degree-of freedom (2DOF and 3DOF) systems with persistent inputs cannot be treated within the framework of the standard configuration. In addition, past treatments of persistent inputs within the framework of the generalised 2DOF configuration focused on solutions which yielded stable error transforms without explicitly requiring the same for controller outputs. In this article, a more general configuration is treated and physical considerations are invoked to justify imposition of the requirement that both the regulated variable z(s) and the controller output u(s) be stable. A persistent input model for which there exists a stabilising controller that makes both z(s) and u(s) stable is called acceptable and the necessary and sufficient condition for such acceptability is determined. Also considered is a persistent input model for which there exists a stabilising controller that makes the controller output, the measured output and the regulated variable stable. Such a model is called strictly acceptable and the necessary and sufficient condition for strict acceptability is given. The subset of all stabilising controllers associated with an acceptable persistent input model is parameterised and this parameterisation is used to formulate an H ₂ optimisation problem with persistent inputs which can then be solved using standard procedures.     

Exact computation of infimum for a class of continuous-time H∞ optimal control problem with a nonzero direct feedthrough term from the disturbance input to the controlled output

A noniterative method for the computation of infimum for a class of continuous-time H_∞ optimal control problem is considered in this paper. The problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems. The method is applicable to systems where (i) the transfer function from the disturbance input to the measurement output is free of imaginary axis invariant zeros and left invertible, and (ii) the transfer function from the control input to the controlled output of the given system is free of imaginary axis invariant zeros and right invertible. The result presented in this paper is a continuation of the previous work of the author and his co-workers (Chen et al., 1992), in which the direct feedthrough term from the disturbance input to the measurement output of the given system are required to be zero.     

Analysis, design, and performance limitations of optimal filtering in the presence of an additional input with known frequency

In this paper, the inputs are considered to be of two types. The first type of input, as in standard H₂ optimal filtering, is a zero mean wide sense stationary white noise, while the second type is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. The generalized H₂ optimal filtering problem seeks to find a linear stable filter that estimates a desired output such that the H₂ norm of the transfer matrix from the white noise input to the estimation error is minimized subject to the constraint that the mean of the error converges to zero for all initial conditions of the given system and filter and for all possible external sinusoidal signals. The analysis, design, and performance limitations of generalized H₂ optimal filters are presented here.     

Transformations of control systems for the investigation of pulse modes

It is considered a scheme of transformation of control system with unbounded velocity hodograph to a system of reduced order (called the derived system) via integral of the limit system which describes behavior of the original one under pulse (practically sufficiently large) control inputs. There are formulated the conditions (connected with controllability of the limit system on its integral manifold) when some solution of the derived system will be a generalized solution of the original one that is it can be approximated by a sequence of regular solutions. Methodical and applied examples are given.