Quantizer design for interconnected feedback control systems

In this paper, we consider the design of interconnected H-infinity feedback control systems with quantized signals. We assume that a decentralized static output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H-infinity disturbance attenuation level is achieved, and that the subsystems’ measurement outputs are quantized before they are passed to the local controller. We propose a localoutput- dependent strategy for updating the quantizers’ parameters, so that the overall closed-loop system is asymptotically stable and achieves the same H-infinity disturbance attenuation level. Both the pre-designed controllers and the quantizers’ parameters are constructed in a decentralized manner, depending on local information.     

具有控制时滞系统的最优无静差正弦扰动抑制

研究在外部正弦扰动作用下,控制含时滞的线性系统的最优无静差调节器设计问题．首先利用Artstein变换将控制变量含时滞的系统转化为不舍时滞的系统;然后利用内模原理构造扰动补偿器,将带扰动的系统转化为无扰动的增广系统,从而将无静差扰动抑制问题转化为无扰动增广系统的最优调节器设计问题;最后利用最优控制理论求得最优无静差反馈控制律．仿真结果表明了所提出方法的有效性．     

On-line hierarchical control for steady-state systems

This paper presents the basic principles and main properties of hierarchical control structures, which can be applied in steady-state optimization of complex systems. An essential feature of the structures considered in this paper is the use of feedback from the controlled system, along with the mathematical models. Suitable iterative procedures, preferably starting from the open-loop optimum, are proposed and investigated at some length. The stress of most of the discussion is on inequality constraints and on model-reality differences, which are unavoidable in any application of computer control.     

On steady-state errors in nonlinear control systems

In a recent paper control systems containing a memoryless nonlinear element are considered, and the steady-state response to certain inputs is characterized when the circle condition for stability is met. Here we give three results for the case in which the forward path contains an additional element, an integrator preceding the nonlinearity.     

Falsification of combined invariance and reachability specifications in hybrid control systems

We propose an abstraction-based method that can be applied to falsify a class of computation tree logic (CTL) specifications that combine invariance and reachability requirements in terms of the discrete state of a hybrid control system. The fragment of CTL that we address is not expressible in ACTL^? (which includes LTL). The method involves applying supervisory control to a finite abstraction of the hybrid system to falsify the specification. For the class of systems that we consider, falsification of the specification implies a flaw in the design of the control and automation logic.     

Double-loop-iterative-tracking-algorithm-based direct coordination for hierarchical steady-state control of interconnected systems

An alternative hierarchical optimization algorithm obtained by combining a double-loop iterative strategy with an efficient coordination task is proposed. The new algorithm derived from the tracking method (Sidaoui et al. 1989, 1991) is applicable to non-convex problems and has the advantage of giving a better rate of convergence. Simulation results are given and compared with the original algorithm, indicating the superiority of the new approach for the example considered.     

The steady-state invertibility and feedforward control of linear time-invariant systems

The notion of steady-state invertibility of a system is introduced, which is concerned about the problem of being able to find an input so that the output of a stable system is asymptotically equal to a specified output of a certain class of functions. Necessary and sufficient conditions are found for a linear time-invariant system to be steady-state invertible. Application of these results is then made to find necessary and sufficient conditions for a feedforward controller to exist for a general linear time-invariant system, so that asymptotic tracking, in the presence of a general class of measurable disturbances occurs. Explicit feedforward controllers which will accomplish this are obtained. Properties of the steady-state invertibility condition are then obtained; in particular, it is shown that a system is "almost always" steady-state invertible if the number of plant inputs is not less than the number of outputs; if the number of plant inputs is less than the number of outputs, then a system is "almost never" steady-state invertible. It is then shown that a system which is minimum phase and which has at least the same number of inputs as outputs is always steady-state invertible.     

Quantization error and design of digital control systems

The evolution of the error caused by the amplitude quantization in digital control systems can be studied by introducing bounded disturbances at the points of the quantization. Such a formulation provides an upper bound for the actual quantization error. This paper introduces the problem of the quantization error in the light of the discrete-time optimum control theory. The determination of the worst possible effect of the error due to quantization is reduced to solving a common optimum control problem; the "worst effect" is defined as the maximum of a chosen performance criterion. For a design, a method is proposed for the minimization of the worst effect of the quantization error. Computational solutions illustrate the presentation.     

Deadbeat control system with time-varying uncertainty: Minimization of worst case steady-state tracking error

This paper poses and solves a new problem of the synthesis of a controller that minimizes the worst case steady-state controlled error in the presence of time-varying unstructured uncertainty. We present an easy, straightforward design method for obtaining a controller that minimizes the worst case steady-state controlled error under the assumption that the plant is strictly proper. The detailed contributions are as follows. First, we derive a new, simple expression for calculating the worst steady-state error, which gives useful and interesting suggestions about the controller design. We then show that the synthesis problem is reduced to a simple and tractable l1 -norm minimization problem. Therefore, this reduction provides a feasible method for solving the design problem of a controller that minimizes the worst case steadystate error. Second, a deadbeat tracking control problem is considered and a straightforward design method is presented for obtaining a deadbeat controller with given settling steps both to guarantee robust stability and to minimize the worst case steady-state error. The proposed controller is easily obtained by solving a simple linear programming problem. Finally, we show that the proposed controller minimizes the maximum error bound of the controlled output to persistent bounded disturbance.     

Recursive second-order approximation method for optimization and control of steady-state systems

A recursive second-order approximation approach for the optimization and control of steady-state systems is proposed. The method constructs the hessian matrix of the real performance by using a modification of the Broyden, Fletcher, Goldfart, and Shanno (BFGS) formula which only uses first-order information of the real process. The iterative direction can be obtained by solving a second-order approximate optimization problem which is determined by a modification of the BFGS formula. To obtain a new iterative point, Newton step and one-dimensional search updating strategies are employed. Global convergence and optimality of the derived algorithms are thoroughly investigated. In particular, the R-superlinear properties of the new approach are verified under local conditions. Numerical results show that the new approach is superior to the sequence model approximation (SMA) method.     

Multivariable quantitative feedback design for tracking error specifications

The use of tracking error specifications in quantitative feedback theory (QFT) design is discussed for multi-input, multi-output (MIMO) systems. These specifications bound the closed loop transfer function within a disk around some nominal (model) performance while preserving the QFT approach that allows treatment of highly structured (and unstructured) uncertainty. Because the specifications capture phase information, the level of over-design in certain MIMO QFT designs is reduced. The method presented allows independent, two-degree-of-freedom design.     

Sequence model approximation approach for optimization and control of steady-state systems

A new approach—a sequence model approximation method—is proposed for determining the optimum steady-state operating point of an industrial process. The method makes full use of first-order information of reality to construct an approximate model which can match real output and the required derivatives of reality at each iteration. In order to ensure that the real objective index descends, the Newton step and a one-dimensional minimization search technique are then used respectively. The approach's convergence and optimality conditions are investigated under mild assumptions. Simulation results show that the new approach requires fewer set-point changes, and exhibits a higher convergent rate than previous methods in this field.     

Piecewise output feedback control for affine systems with disturbances based on linear temporal logic specifications

In the paper,we investigate the problem of finding a piecewise output feedback control law for an uncertain affine system such that the resulting closed-loop output satisfies a desired linear temporal logic (LTL) specification.A two-level hierarchical approach is proposed to solve the problem in a triangularized output space.In the lower level,we explore whether there exists a robust output feedback control law to make the output starting in a simplex either remains in it or leaves via a specific facet.In the higher level,for the triangularization,we construct the transition system according to the reachability relationship obtained in the lower level and search for feasible paths that meet the LTL specification.The control approach is then applied to solve a motion planning problem.     

Adaptive control of accumulative error for nonlinear chaotic systems

We present an adaptive control scheme of accumulative error to stabilize the unstable fixed point for chaotic systems which only satisfies local Lipschitz condition, and discuss how the convergence factor affects the convergence and the characteristics of the final control strength. We define a minimal local Lipschitz coefficient, which can enlarge the condition of chaos control. Compared with other adaptive methods, this control scheme is simple and easy to implement by integral circuits in practice. It is also robust against the effect of noise. These are illustrated with numerical examples.     

New approach to stochastic optimizing control of steady-state systems using dynamic information

An underlying relationship between a dynamic stochastic control system and its steady-state counterpart is thoroughly investigated. A novel approach which uses both dynamic and steady-state information for solving the stochastic steady-state optimizing control problem is presented. A two-stage steady-state system identification technique is proposed and employed in the presented approach to estimate the expectation of the real process derivative. Compared with integrated system optimization and parameter estimation (ISOPE) methods, this new approach has reduced significantly the required controller set point changes and is much less sensitive when subjected to noise. Optimality of the algorithm is examined and sufficient conditions for global convergence are provided. Consistency and asymptotic behaviour of the two-stage identification method are also investigated. Computer simulations are provided and comparisons are made between the ISOPE method and the presented approach. Simulation results show that this new approach is very efficient and reliable.     

Adaptive learning control of linear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output uncertain linear systems when the reference output signal is smooth and periodic with known period T. The considered systems are required to be observable, minimum phase, with known relative degree and known high frequency gain sign. By developing in Fourier series expansion a suitable unknown periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: bounded closed-loop signals and global exponential tracking of both the input and the output reference signals are obtained when the Fourier series expansion is finite, while global exponential convergence of the input and output tracking errors into arbitrarily small residual sets is achieved otherwise. The structure of the proposed controller depends only on the relative degree, the reference signal period, the high frequency gain sign and the number of estimated Fourier coefficients.     

Verification of external specifications of reactive systems

External specification is currently approached by specification languages for describing and analyzing system requirements. The external specification can be defined during the early stages of the system development and can be very useful for: checking the class/system/subsystem requirements; checking the system composition; evaluating costs of reuse; defining validated reference requirements, histories, and traces for the final validation. The paper presents a collection of criteria in order to formally verify the external specification of reactive systems/subsystems. The verification criteria are grounded on the Tempo Reale object-oriented language (TROL) specification model for real-time systems. In TROL, the external specification is expressed in terms of ports and clauses with temporal constraints. The goal of the verification criteria presented is to check the completeness and consistency of the external specification with special attention to temporal constraints. These criteria can be applied to other real-time specification models and have been enforced in the tool object oriented machine state (TOOMS) tool. A practical example illustrates the verification process that embodies these criteria