Adaptive control allocation

In this work we address the control allocation problem for a nonlinear over-actuated time-varying system where parameters affine in the effector model may be assumed unknown. Instead of optimizing the control allocation at each time instant, a dynamic approach is considered by constructing update-laws that represent asymptotically optimal allocation search and adaptation. Using Lyapunov analysis for cascaded set-stable systems, uniform global/local asymptotic stability is guaranteed for the sets described by the system, the optimal allocation update-law and the adaptive update-law.     

Moving horizon control of nonlinear systems with input saturation,disturbances and plant uncertainty

We present a moving horizon feedback system, based on constrained optimal control algorithms, for nonlinear plants with input saturation, disturbances and plant uncertainty. The system is a non-conventional sampled-data system: its sampling periods vary from sampling instant to sampling instant, and the control during the sampling time is not constant, but determined by the solution of an open loop optimal control problem. We show that the proposed moving horizon control system is robustly stable and is capable of attenuating L∞ bounded disturbances.     

Stabilization and second‐order optimization for multimodule impulsive switched linear systems

In this work, we investigate stabilization and optimization issues for a class of multimodule impulsive switched linear systems. First, we establish a necessary and sufficient criterion on asymptotic stabilizability via a pathwise state‐feedback scheme, which achieves the merits of both time‐driven and state‐feedback mechanisms. Then, we present an impulse/switching instant optimization problem that usually arises in finite‐horizon optimal control. To reduce the computational burden, we propose a novel method via developing efficiently computable expressions for the cost function, the gradient vector, and the Hessian matrix. Next, we design a second‐order optimization algorithm searching for the optimal impulse/switching instants. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.     

H∞ output tracking control for uncertain networked control systems via a switched system approach

In this paper, the problem of H_∞ output tracking control for networked control systems with random time delays and system uncertainties is investigated. Effective sampling instant that is tightly related with transmission delay from sensor to actuator is proposed to ensure that the random variable time delay is always shorter than one effective sampling period. By using both active time‐varying sampling period strategy and hybrid node‐driven mechanism, the switching instant is coincided with the effective sampling instant. An augmented time‐varying networked tracking system model is provided by including the output tracking error as an additional state. However, random transmission delay causes indeterminate sampling period, which induces infinite subsystems. Gridding approach is introduced to transform the continuous time axis into discrete‐time sequences, which guarantees the finite number of switching rules. By employing multiple Lyapunov–Krasovskii functions, linear matrix inequality (LMI)‐based output tracking H_∞ performance analysis is presented, and robust switching H_∞ model reference tracking controller for networked control systems with communication constraints and system uncertainties is designed to guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. Finally, simulation results illustrate the correctness and effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

State-space approach to nonlinear predictive generalised minimum variance control

A nonlinear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process, but because of the assumed structure of the system, the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well-known GPC controller.     

A technique for suboptimal feedback control of nonlinear systems

A simple easily implemented method is developed for obtaining a suboptimal control law for the optimization problem associated with minimizing a quadratic cost functional for nonlinear systems. The suboptimal control law is derived using a Taylor's series representation for the feedback gain matrix after modeling the nonlinear system by a linear system at each instant of time. The resultant control law is of feedback form and is nonlinear in state. The suboptimal control is obtained without using iterative techniques or any true optimal solutions. A second-order numerical example illustrates the effectiveness of the method and gives a comparison to the results of previous methods.     

An indirect adaptive controller with a self-excitation capability

An indirect adaptive pole placement controller is presented which stabilizes and asymptotically regulates any discrete-time single-input, single-output linear time-invariant plant which is of known order n , is controllable, and observable, and has unknown parameters. To avoid singular points in the algorithm, the adaptive controller solves the pole-placement design equation asymptotically with time rather than trying to solve it exactly at each time instant. The stability of the adaptive control system and the asymptotic regulation of the plant output to zero are ensured by an additional self-excitation generated by the adaptive controller. A novel kind of an error signal to control the magnitude of the self-excitation is obtained by suitably filtering the self-exciting signal and monitoring changes of the controller parameters as they are generated by the adaptive algorithm     

State space approach to behavioral systems theory: the Dirac–Bergmann algorithm

This paper develops an approach to behavioral systems theory in which a state space representation of behaviors is utilised. This representation is a first order hybrid representation of behaviors called pencil representation. An algorithm well known after Dirac and Bergmann (DB) is shown to be central in obtaining a constraint free and observable (CFO) state space representation of a behavior. Results and criteria for asymptotic stability, controllability, inclusions and Markovianity of behaviors are derived in terms of the matrices of this representation which involve linear algebraic processes in their computation.     

Robustly asymptotically stable finite-horizon MPC

This paper presents a robustly stable finite-horizon model predictive control (MPC) scheme for linear uncertain systems, in which the uncertainty is not restricted to some specific uncertainty class (polytopic, affine, LFT, etc.). The only requirement is that the state-space matrices remain bounded over the uncertainty set. Suitable constraints are added to the MPC cost function to impose robust asymptotic stability and to deal with input/output constraints. The resulting optimization problem is solved at each time instant in a probabilistic framework using an iterative randomized ellipsoid algorithm (REA). The method is compared in simulation to the existing approach of Kothare, Balakrishnan and Morari [(1996). Robust constrained model predictive control using linear matrix inequalities. Automatica, 32(10), 1361–1379].     

On the determination of optimal costly measurement strategies for linear stochastic systems

This paper presents the formulation of a class of optimization problems dealing with selecting, at each instant of time, one measurement provided by one out of many sensors. Each measurement has an associated measurement cost. The basic problem is then to select an optimal measurement policy, during a specified observation time interval, so that a weighted combination of “prediction accuracy” and accumulated “observation cost” is optimized. The current analysis is limited to the class of linear stochastic dynamic systems and measurement subsystems. The problem of selecting the optimal measurement strategy can be transformed into a deterministic optimal control problem. An iterative digital computer algorithm is suggested for obtaining numerical results. It is shown that the optimal measurement policy and the associated “matched” Kalman-type filter can be precomputed, i.e. specified before the measurements actually occur. Numerical results for a third-order system with two possible measurements are presented.     

Robust state‐feedback control of stochastic state‐multiplicative discrete‐time linear switched systems with dwell time

Linear discrete‐time switched stochastic systems are considered, where the problems of mean square stability, stochastic l₂‐gain and state‐feedback control design are treated and solved. Solutions are obtained for both nominal and polytopic‐type uncertain systems. In all these problems, the switching obeys a dwell time constraint. In our solution, to each subsystem of the switched system, a Lyapunov function is assigned that is nonincreasing at the switching instants. The latter function is allowed to vary piecewise linearly, starting at the end of the previous switch instant, and it becomes time invariant after the dwell. In order to guarantee asymptotic stability, we require the Lyapunov function to be negative between consecutive switchings. We thus obtain Linear Matrix Inequalities conditions. Based on the solution of the stochastic l₂‐gain problem, we derive a solution to the state‐feedback control design, where we treat a variety of special cases. Being affine in the system matrices, all the aforementioned solutions are extended to the uncertain polytopic case. The proposed theory is demonstrated by a practical example taken from the field of flight control. Copyright © 2015 John Wiley & Sons, Ltd.     

Routing Permutations on Hypercube Machines with Half-Duplex Links

Algorithms are presented for realizing permutations on a less restrictive hypercube model called the S-MIMD (synchronous MIMD), which allows at most one data transfer on a given communication link at a given time instant, and where data movements are not restricted to a single dimension at a given time. First, an optimal algorithm for bit-permute permutations is developed from a very simple realization of the shuffle on a 3-cube; this algorithm needs 2⌊n/2⌋ routing steps on an n-dimensional hypercube. The technique is then extended to an optimal algorithm for bit-permute-complement permutations, one that needs n routing steps. Also, algorithms are sketched for routing permutations in the classes Ω and Ω⁻¹ in 3⌈n/2⌉ routing steps, yielding an off-line algorithm for routing arbitrary permutations in 3n steps.     

A state-space description for GPC controllers

Generalized predictive control (GPC)-type control algorithms traditionally derived in the polynomial domain are derived in this paper in the state-space domain, but following the polynomial approach due to Clarke et al. (1987). Relations between the polynomial and state-space parameters are presented. Some possible state-space representations which were used earlier in different publications are discussed. The problem of deriving the GPC algorithm in the state-space domain is solved for the unrestricted case as well as for the case of restricted control and output horizons. Some properties of the state estimate for this problem are presented; in particular, two methods of Kalman filtering—optimal and asymptotic—are proposed. The solution is valid for any possible (minimal or non-minimal) state-space representation. Another approach to this problem is by the ‘dynamic programming method’ and solving the Riccati equation (Bitmead et al. 1990). This approach is also presented in this paper but the method differs from this earlier work and does not require extending the state dimension. Ultimately, certain features of the state-space approach are discussed, such as (a) the opportunity for straightforward analysis of the transient states produced by switching on the regulator, by changing the set-point or by changing the regulator parameters; (b) easy extension to the multidimensional case; and (c) the possibility of introducing nonlinearities into the model     

Distributed optimisation for resource allocation with event-triggered communication over general directed topology

This paper focuses on the resource allocation problem(RAP) with constraints under a fixed general directed topology by using the distributed sub-gradient algorithm with event-triggered scheme in multi-agent systems, where each agent owns a cost function and its state value is bounded. The distributed sub-gradient algorithm aims to minimise the total cost by a distributed manner while achieving an optimal solution. Unlike centralised methods, the triggering condition and algorithm for each agent are fully decentralised. At each instant of time, each agent updates its state by employing the states which are collected from itself and its neighbouring agents at their last triggering time. In order to illustrate the effectiveness of the proposed sub-gradient algorithm with event-triggered control law, one simulation example is presented before the conclusion.     

Guaranteed detection of an imbalance instant of the GARCH-process

A detection instant problem of the GARCH-process parametric change with random noise distribution is studied. A sequential procedure of imbalance instant detection, where a decision of change existence is made at a given instant of time after the accumulation of given distinctions between possible process models, is suggested. Formulas for procedure characteristics calculation are developed, asymptotic qualities of the procedure are studied. Model estimated values are presented.     

Enabling cuts on multiresolution representation

Multiresolution representations are widely used in many visualization contexts and applications, since they provide optimal management of the data representation by using at each time instant a level of detail most appropriate for the application requirements. Unfortunately, current solutions do not allow the topology of the object to be changed, and this tends to prevent its adoption in applications where topological changes are needed, such as virtual surgery applications. By extending a known multiresolution model based on simplicial complexes, we develop a new approach which supports dynamic topological modifications of the represented object without greatly increasing the representation complexity.     

The optimal control of an M/G/1 queueing system with server vacations, startup and breakdowns

This paper studies the control policy of the N policy M/G/1 queue with server vacations, startup and breakdowns, where arrivals form a Poisson process and service times are generally distributed. The server is turned off and takes a vacation whenever the system is empty. If the number of customers waiting in the system at the instant of a vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N customers in the system, he requires a startup time before providing service until the system is again empty. It is assumed that the server breaks down according to a Poisson process and his repair time has a general distribution. The system characteristics of such a model are analyzed and the total expected cost function per unit time is developed to determine the optimal threshold of N at a minimum cost.     

具有数据包丢失的离散随机不确定系统的线性最优满阶估值器

研究了具有数据包丢失和随机不确定性离散随机线性系统的状态估计问题.其中数据包丢失是随机的,且满足Bernoulli分布,系统矩阵中的随机不确定性由一个白色乘性噪声来描述.首先,通过配方方法,提出了最小均方意义下的无偏最优线性递推满阶滤波器.所提出的滤波器用到了当前时刻和最近时刻接收到的观测来保证线性最优性.与多项式滤波和增广滤波器相比,本文的滤波器具有较小的计算负担.然后,基于所获得的线性滤波器推导了线性最优预报器和平滑器.进一步研究了线性最优估值器的渐近稳定性,给出了稳态特性存在的一个充分条件.最后,通过两个仿真例子验证了所提估计算法的优越性.     

Trajectory optimization for maneuvering satellites

This paper proposes an algorithm to compute optimal trajectories for a maneuvering satellite by using a nonlinear programming representation of an optimal control problem. In this problem, a satellite must be located at a given final position with given velocity from initial position and velocity without passing a prohibited region such as the atmosphere while achieving minimum fuel consumption. Optimal control theory is applied to obtain a set of ordinary differential equations subject to two-point boundary conditions (TPB) on the adjoint system. Then an exact penalty function method is employed to obtain the optimal trajectories by solving the TPB problem as initial conditions for the adjoint system and an unknown final time are regarded as decision variables. This formulation, where the optimal control technique and the nonlinear programming method are incorporated, permits more systematic and flexible algorithm implementation.     

Optimal Control for a System on a Unit Simplex in Infinite Time

Optimal control for a semilinear system of first-order partial differential equations in infinite time is studied. The values of control variables belong to a finite-dimensional unit simplex at every instant at every point of the space. Necessary and sufficient conditions for the quality criterion of optimal control to be absolutely maximal are formulated.