Control Theory Design Research Articles

Fuzzy adaptive resilient decentralized control of nonlinear interconnected cyber-physical systems under false data injection attacks

In this paper, a new fuzzy adaptive resilient decentralized control method is presented for the nonlinear interconnected cyber-physical systems under false data injection (FDI) attacks. Fuzzy logic systems (FLS) are used to model unknown nonlinear dynamics and the FDI attacks are represented by the sum of the system states and unknown time-varying bounded functions. To deal with the problem of the system states are unavailable under FDI attacks, a new coordinate transformation is proposed for control design. By using the backstepping control design theory and Nussbaum function property, a fuzzy adaptive resilient decentralized control scheme is developed, where the Nussbaum functions are employed to deal with the unknown time-varying weight. Then, the stability of the controlled systems is proved by constructing a appropriate Lyapunov function. Finally, the effectiveness of the proposed fuzzy adaptive resilient decentralized control scheme is verified by the simulation and comparison results.

Design of Generalized H∞-Suboptimal Controllers Based on Experimental and A Priori Data

This paper considers a linear continuous- or discrete-time dynamic object in the absence of its mathematical model. As is demonstrated below, a control law that suboptimally damps initial and (or) exogenous disturbances of such objects can be implemented based on experimental and a priori data. The approach involves the methods of robust control design and duality theory as well as the technique of linear matrix inequalities.

Passivity and Immersion (P&I) Approach for Constructive Stabilization and Control of Nonlinear Systems

This letter proposes a control algorithm as a stepping stone for the stabilization and control of structured and unstructured systems discussed in the literature. The foundation behind this proposed controller design theory utilizes an invariant target manifold giving rise to a non-degenerate form, through which the definition of certain passive outputs and storage functions provide the control law for stabilizing the system. The proposed control framework is developed by integrating the notions of immersion and passivity hence labeled as the “Passivity and Immersion (P&I) approach.” Immersing the system dynamics into the user-defined lower order target dynamics and using the concept of attractivity of the manifold based upon the passivity theory results in encompassing various design paradigms under a single roof of the P&I approach. The benchmark examples are solved to show the effectiveness of the proposed P&I approach in confirming how the various design paradigms can be unified.

Passivity and Immersion (P&I) Approach With Gaussian Process for Stabilization and Control of Nonlinear Systems

The virtual derivatives computation and successive derivations of virtual inputs in an adaptive backstepping controller cause the explosion of complexity. Moreover, the feedback linearization has poor robustness features and necessitates exact estimation of the feedback control law’s coefficients. Due to measurement noise, the model-based estimation techniques for identifying uncertainties result in inaccurate gradient and Hessian calculations. Such limitations lead to model and measurement uncertainties that prevent effective stabilization and control of nonlinear systems. Machine learning-based data-driven approaches offer effective tools for identifying dynamical systems and uncertainties with minimal prior knowledge of the model structure. Therefore, the contribution of this research is two-fold: First, the general controller design theory is proposed which utilizes the idea of an invariant target manifold giving rise to a non-degenerate two form, through which the definition of certain passive outputs and storage functions leads to a generation of control law for stabilizing the system. Since the above concepts are linked with the Immersion and Invariance (I&I) design policy and the passivity theory of controller design, the proposed methodology is labeled as the "Passivity and Immersion (P&I) based approach". Second, the proposed P&I approach is integrated with a Bayesian nonparametric approach, particularly the Gaussian Process for stabilization and control of the partially unknown nonlinear systems. The effectiveness of the proposed methodologies has been evaluated on an inverted pendulum using MATLAB in the presence of input-output uncertainties.

Fuzzy set theory for optimal design in controlling underactuated dynamical systems with uncertainty

The fuzzy set theory for optimal control design of underactuated dynamical systems with uncertainty is proposed. The uncertainty is (possibly fast) time varying whose bound is unknown and lies in a prescribed set expressed by a fuzzy set. Control goals of uncertain dynamical systems are formulated as a series of constraints, which may be holonomic and nonholonomic. From the view of constraint-following control, we design an adaptive robust control based on a creative uncertainty decomposition, which divides the uncertainty into matched and mismatched terms. This decomposition renders the mismatched term to “disappear” in the stability analysis. The proposed control is able to drive the system to approximately follow the constraints and guarantee system performance (uniform boundedness and uniform ultimate boundedness), in the presence of the uncertainty. It is in deterministic form and not “if–then” fuzzy rules based. Because of the expressed fuzzy set of the uncertainty bounds, a performance index, which balances the conflict between system performance and control cost, can be constructed. An optimal design gain can be obtained by minimizing the performance index whose solution is guaranteed to always exist. Numerical results on a planar vertical takeoff and landing aircraft are presented for demonstration.

Fusion of reinforcement learning and analytical controller design theory for a class of nonlinear

Fusion of reinforcement learning and analytical controller design theory for a class of nonlinear

Optimizing constraint obedience for mechanical systems: Robust control and non-cooperative game

This paper focuses on the optimization of constraint obedience for mechanical systems based on robust control design and non-cooperative game theory. The (possibly fast) time-varying but bounded system uncertainty is considered. First, it aims at a controller to drive the concerned system to follow a set of prescribed constraints. A problem of constraint-following is formulated with a β-measure as the gauge of constraint-following error, and then a robust control with two tunable parameters is proposed to render the measure to be uniformly bounded and uniformly ultimately bounded. Second, it aims at the optimal design of control parameters. A two-player non-cooperative game is formulated with two cost functions, each of which is dominated by one tunable parameter and consists of three parts: the state cost, the time cost and the control cost. Finally, the Nash equilibrium (i.e., the optimal control parameters) is obtained by minimizing the cost functions. By this, the optimization of constraint obedience for mechanical systems is achieved with the existence, uniqueness, and analytical expression of the Nash equilibrium.

Model Reference Adaptive Control Design for Nonlinear Plants

In this paper, the basic theory of the model reference adaptive control design and issues of particular relevance to control nonlinear dynamic plants with a relative degree greater than or equal to one with unknown parameters are detailed. The studied analysis was motivated through its application to a robot manipulator with six degrees of freedom. After linearization using the input-output feedback linearization and decoupling algorithm, the nonlinear Multi-input Multi-output system was transformed into six independent single-input single-output linear subsystems each one has a relative degree equal to two, the obtained results in different simulations shows that the augmented reference model adaptive controller has been successfully implemented.

The Impact of Voltage Regulation of Multiinfeed VSC-HVDC on Power System Stability

Due to the anticipated proliferation of HVDC links up to and beyond 2020 into transmission systems, it is expected that in some locations, two or more HVDC links will be installed with a short electrical distance between them and will form a multiinfeed (MI)-HVDC scenario for the system. The control and operation of MI-HVDC systems are of particular concern for weak grids such as that likely to be found in the North of Scotland network. It is shown that the ac voltage regulation in the VSC-HVDC link may adversely affect the dynamic performance of the host weak ac system under the MI-HVDC scenario. To overcome this identified limitation associated with the ac voltage controller in the VSC-HVDC link, a new controller modification conforming to the grid code is proposed in this paper. Furthermore, this paper presents a robust control design method for ac voltage control using the fractional order (FO) control design theory. The influences of the proposed FO-based ac voltage controller are assessed alongside various voltage controllers for the representative North Scotland system. It is shown that the FO-based ac voltage controller has favorable effects on the dynamic behavior of weak ac systems with MI-HVDC.

Practical Methods for Aircraft and Rotorcraft Flight Control Systems: An Optimization-Based Approach [Bookshelf

This book provides information covering the fundamentals of control theory and optimization applied to real-world flight control systems. Covers the following topics: the challenges inherent in flight control system design; an overview of their core approach to flight control system design utilizing multiobjective parametric optimization; the specific software developed called Control Designer’s Unified Interface (CONDUIT); detailed explanations of the tools, plots, language, and four key components involved in defining the problem using CONDUIT; the XV-15 hover/forward flight case study is discussed in sufficient detail for even seasoned veterans to find the presentation informative and useful. Here the authors have done an excellent job of demonstrating many flight control concepts; proprietary specifications; methodologies for developing simulation models of model-based flight control system designs; design of flight control systems; the inner workings of the design optimization approach. The coverage includes specifics of various algorithms, along with their relative advantages and disadvantages. This chapter also provides insights into sequential loop closure strategies, with emphasis on their effectiveness and practical use; nested versus simultaneous multiloop strategies; and design considerations for real-world applications. This book serves as an excellent reference for senior undergraduate and/or graduate students, and it provides a wellbalanced perspective covering the theory, implementation, and practical applications of flight control design.

Review and recent development of internal model design

Robust output regulation is a controller design theory for achieving reference tracking and disturbance rejection as well as system stability. The main feature of the theory is that the reference and/or disturbance signals have explicit structural description, especially by an exosystem. By decoding this structural information, the desired steady state/input of the system can be completely characterised, albeit not measurable or implementable due to system uncertainty. The steady state/input description simply copies the exosystem dynamics for simple systems, however, it relies on more complicated steady-state generators in most non-linear scenarios. Once the steady state/input is characterised, it can be estimated by an internal model. Proper construction of internal model can well compensate for the desired steady state/input resulting in a stabilisation problem about an equilibrium point. The control objective is achieved if such a stabilisation problem is solved. This paper does not ambitiously aim at a complete overview picture of the three decade development of output regulation theory. It attempts to show a small trail in the garden of vast collections of output regulation results that may lead the audience from simple to advanced internal model design techniques. In particular, it reviews the simple PID structure, the p-copy internal model for linear systems, various internal models for non-linear systems, and the recent development of generalised internal model to accommodate adaptive scheme.

Finite-time sliding mode control design for a class of uncertain conic nonlinear systems

This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness U+0028 FTB U+0029 based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities U+0028 LMIs U+0029, which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control U+0028 SMC U+0029 law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.

An Intelligent Design for a PID Controller for Nonlinear Systems

AbstractThe proportional integral derivative (PID) controller is the most frequently used controller design for industrial applications because of its favorable response and simplicity of adjustment. However, PID manual tuning is traditionally based on engineering experience, and adjusting nonlinear or unknown systems is extremely difficult. In promoting an intelligent controller design theory that can be applied to the control of various systems, this paper proposes a nonlinear control design method that involves determining the optimal solution and obtaining the transfer function of an unknown system by using sequential quadratic programming. In addition, this paper presents a case study of an induction motor V/F speed control to demonstrate the effectiveness of the proposed method based on MATLAB simulation. The results prove that the design of the proposed intelligent PID controller is more robust than traditional controller designs.

A robust wheel slip ratio control design combining hydraulic and regenerative braking systems for in-wheel-motors-driven electric Vehicles

This paper develops a robust wheel slip controller for in-wheel-motors-driven electric vehicles equipped with both hydraulic anti-lock braking systems (ABS) and regenerative braking (RB) systems. Based on a combination of optimal predictive control design and Lyapunov theory, the issue of uncertain vehicle parameters is well addressed. A novel braking torque distribution strategy is also introduced to achieve smooth regulation of the hydraulic pressure, such that pedal pulsating effect of the traditional ABS system can be relieved. By utilizing the larger working range of the hydraulic braking (HB) system and the faster response of the RB system, a better wheel slip control performance can be obtained. Moreover, the torque distributer helps to reach a good compromise between braking distance and the magnitude of the RB torque, which is directly related to the amount of regenerated energy. The effectiveness of the proposed control system has been validated in various simulations.

Generalized Synchronization of Typical Fractional Order Chaos System

Based on the fractional calculus predictor-corrector algorithm and control design theory, generalized synchronization of dynamics of a chaotic system is investigated by linear or nonlinear feedback control, making the non-linear chaotic synchronization error system become linear systems, then synchronous controller was designed based on the stability theory of fractional linear systems [10], and the generalized synchronization of fractional order chaotic systems was fulfilled in different structures and the different order. The auxiliary system method is simple and effective. Detailed n umerical results verify the effectiveness of our proposed new scheme.

Robust controller design based on generalized Bode envelopes

We propose simple tools for robust design of controllers for SISO linear systems with or without uncer- tainty. These tools are based on the generalization of frequency domain, where the uncertainty is defined by generalized Bode envelopes (GBE). The utilization of generalized Nyquist and Mikhailov theorems, which uses the number of GBE crossings with certain predefined horizontal lines, to deduce stability, allows to obtain stability as well as performance specifications simultaneously. The same design rules can be applied to continuous as well as discrete time systems. We provide examples to demonstrate our method of controller design for various control systems. The main problem of control theory is a design of an appropriate controller for a given plant with prescribed specifications. The controller should be robust enough to manage the errors in the model, noise and disturbances. Then, the designed controllers can be used in diverse applications ranging from automotive to process control. In the classical control design theory (e.g., Bode (1945)), the noise and uncertainties are not explicitly modeled, thus the phase and gain margins are used to make the system more robust. In the modern optimal control Kwakernaak & Sivan (1972), the specifications are converted to some performance criterion that should be minimized. In our approach, we avoid the need in gain and phase margins by exploring the poles and zeros clustering in the complex plane. If all the poles in the closed loop are clustered inside an arbitrary chosen bounded region G , we say that this system is G stable and all the specifications are met. To provide better stability margins we may choose the location of the region farther to the left from the imaginary axis (for continuous systems). By choosing the region inside the unit circle, we can use the same tools to design discrete controllers for discrete plants. Further development of the robust design went in a few directions described below. The parametric methods of robust control are described in Bhattacharyya et al. (1995), and Barmish (1993). In these methods, the structure of uncertainty is defined aforehand, and the design procedure is based on alge- braic and optimization methods. Another type which is based on H ¥ norm was proposed by Zames (1981). A loop shaping in frequency domain that is based on H ¥ theory was proposed by McFarlane et al. (1992). The methods of loop shaping try to consider the sensitivity at low and high frequencies in the design. A more recent approach is based on the linear matrix inequalities (LMI) (e.g., Iwasaki & Hara (2004)), but this approach uses state space representation and not a transfer function. Our aim is to fill the gap between the traditional classical control design theory, and more mathematically inclined sophisticated modern robust control theory. One of the earliest attempts to explicit plant uncertainty description was formulated in the quanti- tative feedback theory (QFT) by Horowitz (2001). In this theory, the fixed controller structure is not assumed, and the design is made by utilization of Nichols chart and conversion of the specifications to the frequency domain. Similarly to QFT, our method is very intuitive allowing a designer to achieve the desired performance and to see what trade-offs are necessary. In contrast to QFT, we use generalized

Theory and Software Package for Simulation and Smart Control Design for Complex Flexible Aerospace Vehicles

AbstractNew results in the field of the automaton of the aerospace flight control system design are presented in this paper. The concept of a universal program for research of dynamic properties, calculation of comprehensive mathematical models, and simulation of the flight motion and synthesis of smart control laws for different types of the flexible aerospace constructions (launchers and missiles) is considered. The special attention to creation of mathematical models of different physical phenomenon of aerospace vehicles is given. The basis of the program is the structure, which allows carrying out of the analysis of dynamic characteristics, simulation, and visual information representation. The software package is supplied with the library of program modules. These modules are designed on the base of mathematical models of separate vehicle elements and different physical effects, such as flexibility, sloshing, sluggishness of engines, local angle of attack values, etc. Selection of different sets of the mathematical models and program modules allows investigating different constructions for known and prospective vehicles. The interface of the program enables changing parameters of the vehicle in a wide range, to simulate flight at any trajectory and to output results of the analysis in a digital or graphical form. For synthesis of control laws, provides the usage of the smart control approach.

Discrete time integral sliding mode control for overhead crane with uncertainties

This study firstly addresses an integral sliding mode control method for discrete time systems. The underlying continuous system is affected by both matched and unmatched uncertainties. The past value of the disturbance signal is taken as the estimate of its present value. The sliding mode controller is designed to ensure the existence of sliding mode in the presence of uncertainties. The proportional part is designed based on the analysis of closed-loop stability conditions. The controller design theory above is applied to an overhead crane system in later sections. The overhead crane system, which is a familiar control problem is described by a linear model, the parameters of which are estimated. It is affected by uncertainties such as friction, swing of the load and non-linearities because of changing rope length. Both simulation and experimental results are reported. The efficacy and robustness of the proposed controller are demonstrated.

Linearization: Students Forget the Operating Point

Linearization is a standard part of modeling and control design theory for a class of nonlinear dynamical systems taught in basic undergraduate courses. Although linearization is a straight-line methodology, it is not applied correctly by many students since they often forget to keep the operating point in mind. This paper explains the topic and suggests a way to improve the teaching of the methodology in control courses. The idea is presented on a model of an inverted pendulum on a cart—a classical laboratory model used in the control theory education process.

State-Space Approximations of the Orr-Sommerfeld System with Boundary Inputs and Outputs

Finite-dimensional state-space approximations of the Orr–Sommerfeld equation for plane Poiseuille flow with boundary input and output are discretized to state-space models using two spectral techniques. The models are compared for accuracy and discussed in the context of metrics important for a nonnormal dynamical system. Both state-space models capture the sensitivity behavior of the pole-zero perturbations and the pseudospectrum properties. The effects of balanced truncation ordered by Hankel singular values are discussed. For practical purposes, both methods are effective, and yet certain basic variations in the state-space properties exist. The merits and penalties of the two techniques are also provided. I. Introduction D ISTRIBUTED-PARAMETERS dynamical systems are described by partial differential equations (PDE) with associated boundary conditions. These systems are solved by numerical discretization to yield sets of ordinary differential equations similar to those in lumped-parameters systems [1,2]. This paper considers the state-space modeling of the two-dimensional (2-D) perturbations of plane Poiseuille flow described by the well-known Orr– Sommerfeld (OS) equation with the incorporation of an input/output structure. Two different spectral techniques are evaluated here. Of interest is existence of some basic variation in the state-space properties consisting of certain nontruncatable superdamped eigenvaluesandaninputfeedthroughtermintheoutputequation.Astrong motivation exists todemonstrate the effectiveness of using the finitedimensional state-space approximations in representing an infinitedimensional system. The state-space representation is increasingly popular,becausenumeroustoolboxeshavebeendevelopedbasedon the state-space form. MATLAB®, for example, offers toolboxes for balancing, model reduction, control design, data analysis, Simulink, and system theory [3]. All require standard state-space representation.Foraplanegeometry,spectraltechniques[4,5]arepowerfulin constructing state-space models. These are the original models that represent the infinite-dimensional systems. For certain flows, excitable by the input and observable through the output, the original models can be further balanced and order reduced. The balanced reduced-order models (BROMs) are commonly used in designing estimators and controllers. The OS system is of interest in flow controls, in association with thefundamentalproblemoftransitiontoturbulencein fluid flows ata much lower Reynolds number than the ones predicted by linear stability theory [6]. For the plane Poiseuille flow, the OS differential operators are highly nonnormal [7,8]. It is well known that, for nonnormal systems, the eigenvalues alone are inadequate to predict the stability of the flow. It can be demonstrated that, even when all eigenmodes are damped, large bursts of transient responses (orders of magnitude greater than the excitations) can be generated for certain transfer functions of a nonnormal system. Although exerting no exponential growth, these large transient bursts are believed as capable of triggering a transition to turbulence via a subcritical route to instability [6–8]. The aim of this paper is to compare and validate two spectral techniques applied to the OS system and to point out the basic differences between the eigenvalue properties and the state-space representations. A second aim is to demonstrate the sensitivity of the nonnormality of the OS operator [7] and of the transfer function, as well as to show the effects of balanced model truncation.