Globally stable PID-like control of mechanical systems

Decoupled PID control with actuator constraints and velocity measurement or estimation achieves global asymptotic stability of the desired configuration, if there is some friction in the controlled mechanical system and the signals to be integrated are limited accordingly. Stability analysis using the direct Lyapunov method and Gershgorin's “circle theorem” gives these limits and physically meaningful lower bounds on position control gains. A simple procedure is proposed for selecting the design parameters and determining the gains of the controllers.     

High-gain robust adaptive controllers for multivariable systems

This paper extends the switching free high-gain stabilizing adaptive control rules of Byrnes and Willems to a wide class of adaptive schemes capable of tolerating nonlinear state feedback perturbations.     

Globally stabilizing adaptive control design for nonlinearly-parameterized systems

In this note, a new adaptive control design is proposed for nonlinear systems that are possibly nonaffine and contain nonlinearly parameterized unknowns. The proposed control is not based on certainty equivalence principle which forms the foundation of existing and standard adaptive control designs. Instead, a biasing vector function is introduced into parameter estimate; it links the system dynamics to estimation error dynamics, and its choice leads to a new Lyapunov-based design so that affine or nonaffine systems with nonlinearly parameterized unknowns can be controlled by adaptive estimation. Explicit conditions are found for achieving global asymptotic stability of the state, and the convergence condition for parameter estimation is also found. The conditions are illustrated by several examples and classes of systems. Besides global stability and estimation convergence, the proposed adaptive control has the unique feature that it does not contains any robust control part which typically overpowers unknown dynamics, may be conservative, and also interferes with parameter estimation.     

Nonlinear design of adaptive controllers for linear systems

A new approach to adaptive control of linear systems abandons the traditional certainty-equivalence concept and treats the control of linear plants with unknown parameters as a nonlinear problem. A recursive design procedure introduces at each step new design parameters and incorporates them in a novel Lyapunov function. This function encompasses all the states of the adaptive system and forces them to converge to a manifold of smallest possible dimension. Only as many controller parameters are updated as there are unknown plant parameters, and the dynamic order of the resulting controllers is no higher (and in most cases is lower) than that of traditional adaptive schemes. A simulation comparison with a standard indirect linear scheme shows that the new nonlinear scheme significantly improves transient performance without an increase in control effort     

Design of stable decentralized adaptive model-following controllers for large-scale systems

A decentralized model reference adaptive control for a class of large-scale inter-connected systems is developed. The proposed scheme does not require identification of the system parameters, or satisfaction of perfect model-following conditions (PMFC). The boundedness of the output error and the controller parameters is guaranteed using Lyapunov stability theory. The effectiveness of the developed algorithm is demonstrated using a numerical example.     

A performance comparison of robust adaptive controllers: linear systems

We consider robust adaptive control designs for relative degree one, minimum phase linear systems of known high frequency gain. The designs are based on the dead-zone and projection modifications, and we compare their performance w.r.t. a worst case transient cost functional with a penalty on the ^∞ norm of the output, control and control derivative. We establish two qualitative results. If a bound on the ^∞ norm of the disturbance is known and the known a priori bound on the uncertainty level is sufficiently conservative, then it is shown that a dead-zone controller outperforms a projection controller. The complementary result shows that the projection controller is superior to the dead-zone controller when the a priori information on the disturbance level is sufficiently conservative.     

Uniformly ultimately bounded fuzzy adaptive tracking controllers for uncertain systems

Fuzzy adaptive tracking controllers for a class of uncertain nonlinear dynamical systems are proposed and analyzed. The controllers consist of adaptive and robustifying components whose role is to ify the effects of uncertainties and to achieve a desired tracking performance. The interactions between the two components have been investigated. The closed-loop system driven by the proposed controllers is shown to be stable with all the adaptation parameters being bounded. In particular, the proposed controllers guarantee uniform ultimate boundedness of the tracking error and the time bound of the uniform ultimate boundedness is obtained. An upper bound on the steady-state tracking error is obtained as a function of the gain of the robustifying term and the parameters of the adaptive component. The controllers are tested on an inverted pendulum and simulation results are included. A comparison of the proposed controllers with the ones in the literature is conducted.     

Comparison of adaptive controllers

The paper investigates adaptive control of discrete-time processes satisfying first-order linear difference equations with random coefficients which may be constant or time-varying. Structural relationships between sub-optimal adaptive control laws are discussed and results of systematic Monte-Carlo simulations are reported. These lead to a comparison of two sub-optimal adaptive controls ($\text{‘}\text{optimal}\text{-k-}\text{step-ahead}$’ and ‘self-tuning’) and to conclusions about the need for and effectiveness of adaptive control of the systems simulated. It is conjectured that the results and the classification scheme they suggest might have more general validity.     

Globally convergent adaptive pole assignment for a class of non-minimum-phase stochastic systems

A key difficulty of the explicit approach to self-tuning control—both theoretically and computationally—is the need to solve a polynomial identity to generate the required controller coefficients. For systems with uncorrelated output noise, however, the identity has a simple solution, and in this paper the implications of this phenomenon are discussed in relation to self-tuning regulation. A suitable explicit algorithm is introduced, and it is shown that, under certain conditions, global stability and system identifiability can be established without recourse to sophisticated estimator management techniques.     

On the stability of continuous-time adaptive controllers for pure delay systems

We analyse the stability properties of the linear retarded differential-difference equation (RDDE) that arises in the study of adaptive control of pure delay systems. Three different results are given. Firstly, using Floquet theory necessary and sufficient conditions for stability are established for the case of periodic signals of specified frequencies. Secondly, the theory of averaging is used to derive stability-instability conditions under slow adaptation. Finally, a globally stable modified adaptive regulator for systems with known, possibly time-varying, time delay is presented. Two alternative proofs of the latter results are given. One based on the method of Lyapunov functionals and the second one using a Razumikhin-type theorem.     

Stable genetic adaptive controllers for multivariable systems using a two-degree-of-freedom topology

This paper introduces an adaptive reference tracking controller based on the online genetic estimation of the parameters of the system. The main novelty of the paper relies on the fact that the stability of the genetic adaptive scheme is analytically proved and not simply validated by means of simulation as it is customary in the literature. The resulting set-up is flexible enough to be integrated within a great variety of genetic estimation algorithms, which can in many cases outperform traditional estimation procedures. The goal is achieved by using a certain two-degree-of-freedom (2-DOF) based implementation of the control law in which the reference tracking property is separated from the closed-loop stability. Within this framework, the here-presented procedure for the genetic controller synthesis just affects two time-varying pre-filter blocks that do not compromise the closed-loop stability under weak conditions. In this manner, the power and versatility of genetic algorithms can be safely used to achieve tracking performance disregarding stability, which is delegated to a static feedback controller designed on the basis of robust control theory.     

Stable auto-tuning of hybrid adaptive fuzzy/neural controllers for nonlinear systems

In direct adaptive control, the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller. In the indirect case, however, we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities. In both cases, “approximators” such as linear mappings, polynomials, fuzzy systems, or neural networks can be used as either the parameterized nonlinear controller or identifier model. In this paper, we present an algorithm to tune the adaptation gain for a gradient-based hybrid update law used for a class of nonlinear continuous-time systems in both direct and indirect cases. In our proposed algorithm, the adaptation gain is obtained by minimizing the instantaneous control energy. Finally, we will demonstrate the performance of the algorithm via a wing rock regulation example.     

Stability and robustness properties of universal adaptive controllers for first-order linear systems

Quite recently, examples of non-linear adaptive controllers have been found that adaptively stabilize any scalar first-order linear system. In this paper we describe two general classes of such ‘universal’ adaptive stabilizers that include the previously proposed controllers as special cases, Different types of perturbations of these controllers are studied and we report on extensive simulation experiments. Our results demonstrate considerable qualitative differences in the dynamical behaviour of various adaptive universal stabilizers. While the previously proposed controllers all exhibit the bursting phenomena, we give an explicit example of a stabilizing controller that does not show bursting behaviour.     

Stable auto-tuning of adaptive fuzzy/neural controllers for nonlinear discrete-time systems

In direct adaptive control, the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller. In the indirect case, however, we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities. In both cases, "approximators" such as linear mappings, polynomials, fuzzy systems, or neural networks can be used as either the parameterized nonlinear controller or identifier model. In this paper, we present algorithms to tune some of the parameters (e.g., the adaptation gain and the direction of descent) for a gradient-based approximator parameter update law used for a class of nonlinear discrete-time systems in both direct and indirect cases. In our proposed algorithms, the adaptation gain and the direction of descent are obtained by minimizing the instantaneous control energy. We will show that updating the adaptation gain can be viewed as a special case of updating the direction of descent. We will also compare the direct and indirect adaptive control schemes and illustrate their performance via a simple surge tank example.     

Globally decentralized adaptive backstepping neural network tracking control for unknown nonlinear interconnected systems

A globally stable decentralized adaptive backstepping neural network tracking control scheme is designed for a class of large‐scale systems with mismatched interconnections. Under the assumption that the subsystems share the reference signals from the other subsystems, neural networks are used to approximate the unknown interconnections dependent on all reference signals such that the NN approximation domain can be determined a priori based on the bounds of reference signals. The proposed control approach can guarantee that all closed‐loop signals are globally uniformly ultimately bounded and that the tracking errors converge to a small residual set around the origin. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exploiting timed automata based fuzzy controllers for designing adaptive intrusion detection systems

Network intrusion detection systems (NIDSs) are pattern recognition problems that classify network traffic patterns as either ‘normal’ or ‘abnormal’. Precisely, the main aim of intrusion detection is to identify unauthorized use, misuse, and abuse of computers by detecting malicious network activities such as port scans, denial of service or other attempts to crack computer network environments. Even though the incorporation of conventional Soft Computing techniques in NIDSs has yielded to good solutions, the strong dynamism characterizing network intrusion patterns tend to invalidate the usability of existing framework. To tackle this issue, our proposal performs an adaptive supervised learning on a collection of time series that characterizes the network behavior to create a so-called timed automata-based fuzzy controller (TAFC), i.e. an evolvable fuzzy controller whose dynamic features allow to design an advanced network intrusion detection system able to directly deal with computer network dynamism and support networks’ administrators to prevent eventual damages coming from unauthorized network intrusion. As will be shown in experiments, where our approach has been compared with a conventional Mamdani fuzzy controller, the proposed system reduces the detection error and, as consequence, improves the computer network robustness.     

Nonlinear adaptive control for power integrator triangular systems by switching linear controllers

In this paper, a nonlinear adaptive stabilizer is designed for a class of power integrator triangular systems with the following four features: (i) the chained integrators have the powers of positive odd numbers, which makes the linearization of the studied system uncontrollable; (ii) the nonlinear function contains the virtual control variables; (iii) the bound of the nonlinear parameters entering the function nonlinearity is not required to be known a priori; and (iv) there exists an unknown control coefficient with the unknown bound in the control channel. Our proposed adaptive controller is a switching type controller, in which the designed adaptive stabilizer takes a two‐step procedure: a linear stabilizing controller containing the tuning gains is first designed by the adding a power integrator technique. Switching logic is then proposed to tune online the gains in a switching manner. The proposed adaptive controller globally asymptotically stabilizes the considered system in the sense that, for any initial conditions, the state converges to the origin while all the signals of the closed‐loop system are bounded. Simulation studies clarify and verify the approach. Copyright © 2014 John Wiley & Sons, Ltd.     

A two-stage design of adaptive fuzzy controllers for time-delay systems with unknown models

In this article, a systematic two-stage design method for adaptive fuzzy controllers is presented. The proposed control scheme has low computational complexity. Moreover, the exact mathematical model of the plant to be controlled is not required. The fuzzy controller under consideration is based on the proportional-derivative fuzzy control scheme and triangular membership functions. In the design procedure, the domain intervals of the input and output variables are selected with a heuristic approach to minimize a cost function under the constraint of tolerable overshoots in the response curve. A learning scheme is then proposed to automatically adjust the parameters in the fuzzy controller to reduce the error of the system. It can also be used adaptively to improve the system performance of a time-varying system. Simulations and comparisons are included to demonstrate the effectiveness of the proposed method.     

Design of decentralised adaptive sliding mode controllers for large-scale systems with mismatched perturbations

Based on the Lyapunov stability theorem, a methodology for designing a decentralised adaptive sliding mode control scheme is proposed in this paper. This scheme is implemented for a class of large-scale systems with both matched and mismatched perturbations. The perturbations and the interconnection terms are assumed to be norm bounded under certain mild conditions. The decentralised sliding surfaces with adaptive mechanisms embedded are specially designed for each subsystem, so that when each subsystem enters the sliding mode, the mismatched perturbations and the effects of interconnections can be effectively overcome and achieve asymptotic stability. The decentralised controller with embedded adaptive mechanisms is capable of driving the controlled state trajectories into the designated sliding surface in finite time. This is also achieved without the knowledge of upper bounds of the perturbations except those of the uncertainties in the input channels. A numerical example is included to demonstrate the feasibility of the proposed control scheme.     

LQ performance bounds for adaptive output feedback controllers for functionally uncertain nonlinear systems

We consider functionally uncertain systems which can be written in an output feedback form, where the nonlinearities are functions of the output only. The uncertainty is described by a weighted L² norm about a nominal system, and an approximate adaptive design is given which ensures output practical stability. The main result requires knowledge of the weighted L² uncertainty level. An upper bound on the LQ performance of the output transient and the control input is derived, where the cost penalises the output transient and the control effort on the time interval where the output lies outside the prescribed neighbourhood of zero to which we achieve convergence.