Decentralised adaptive control of a class of hidden leader–follower non-linearly parameterised coupled MASs

In this study, decentralised adaptive control is investigated for a class of discrete-time non-linear hidden leader–follower multi-agent systems (MASs). Different from the conventional leader–follower MAS, among all the agents, there exists a hidden leader that knows the desired reference trajectory, while the follower agents know neither the desired reference signal nor which is a leader agent. Each agent is affected from the history information of its own neighbours. The dynamics of each agent is described by the non-linear discrete-time auto-regressive model with unknown parameters. In order to deal with the uncertainties and non-linearity, a projection algorithm is applied to estimate the unknown parameters. Based on the certainty equivalence principle in adaptive control theory, the control for the hidden leader agent is designed by the desired reference signal, and the local control for each follower agent is designed using neighbourhood history information. Under the decentralised adaptive control, rigorous mathematical proofs are provided to show that the hidden leader agent tracks the desired reference signal, all the follower agents follow the hidden leader agent, and the closed-loop system eventually achieves strong synchronisation in the presence of strong couplings. In the end, the simulation results show the validity of this scheme

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Global parameter identification and control of nonlinearly parameterized systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2002.Includes bibliographical references (leaves 109-114).Nonlinearly parameterized (NLP) systems are ubiquitous in nature and many fields of science and engineering. Despite the wide and diverse range of applications, there exist relatively few results in control systems literature which exploit the structure of the nonlinear parameterization. A vast majority of presently applicable global control design approaches to systems with NLP, make use of either feedback-linearization, or assume linear parameterization, and ignore the specific structure of the nonlinear parameterization. While this type of approach may guarantee stability, it introduced three major drawbacks. First, they produce no additional information about the nonlinear parameters. Second, they may require large control authority and actuator bandwidth, which makes them unsuitable for some applications. Third, they may simply result in unacceptably poor performance. All of these inadequacies are amplified further when parametric uncertainties are present. What is necessary is a systematic adaptive approach to identification and control of such systems that explicitly accommodates the presence of nonlinear parameters that may not be known precisely. This thesis presents results in both adaptive identification and control of NLP systems. An adaptive controller is presented for NLP systems with a triangular structure. The presence of the triangular structure together with nonlinear parameterization makes standard methods such as back-stepping, and variable structure control inapplicable. A concept of bounding functions is combined with min-max adaptation strategies and recursive error formulation to result in a globally stabilizing controller.(cont.) A large class of nonlinear systems including cascaded LNL (linear-nonlinear-linear) systems are shown to be controllable using this approach. In the context of parameter identification, results are derived for two classes of NLP systems. The first concerns systems with convex/concave parameterization, where min-max algorithms are essential for global stability. Stronger conditions of persistent excitation are shown to be necessary to overcome the presence of multiple equilibrium points which are introduced due to the stabilization aspects of the min-max algorithms. These conditions imply that the min-max estimator must periodically employ the local gradient information in order to guarantee parameter convergence. The second class of NLP systems considered in this concerns monotonically parameterized systems, of which neural networks are a specific example. It is shown that a simple algorithm based on local gradient information suffices for parameter identification. Conditions on the external input under which the parameter estimates converge to the desired set starting from arbitrary values are derived. The proof makes direct use of the monotonicity in the parameters, which in turn allows local gradients to be self-similar and therefore introduces a desirable invariance property. By suitably exploiting this invariance property and defining a sequence of distance metrics, global convergence is proved. Such a proof of global convergence is in contrast to most other existing results in the area of nonlinear parameterization, in general, and neural networks in particular.by Aleksandar M. KojiÄ.Ph.D

Adaptive control for time-varying systems: congelation and interconnection

This thesis investigates the adaptive control problem for systems with time-varying parameters. Two concepts are developed and exploited throughout the thesis: the congelation of variables, and the active nodes. The thesis first revisits the classical adaptive schemes and explains the challenges brought by the presence of time-varying parameters. Then, the concept of congelation of variables is introduced and its use in combinations with passivity-based, immersion-and-invariant, and identification-based adaptive schemes are discussed. As the congelation of variables method introduces additional interconnection in the closed-loop system, a framework for small-gain-like control synthesis for interconnected systems is needed.\vspace{2ex} To this end, the thesis proceeds by introducing the notion of active nodes. This is instrumental to show that as long as a class of node systems that possess adjustable damping parameters, that is the active nodes, satisfy certain graph-theoretic conditions, the desired small-gain-like property for the overall system can be enforced via tuning these adjustable parameters. Such conditions for interconnected systems with quadratic, nonlinear, and linearly parametrized supply rates, respectively, are elaborated from the analysis and control synthesis perspectives. The placement and the computation/adaptation of the damping parameters are also discussed. Following the introduction of these two fundamental tools, the thesis proceeds by discussing state-feedback designs for a class of lower-triangular nonlinear systems. The backstepping technique and the congelation of variables method are combined for passivity-based, immersion-and-invariance, and identification-based schemes. The notion of active nodes is exploited to yield simple and systematic proofs. Based on the results established for lower-triangular systems, the thesis continues to investigate output-feedback adaptive control problems. An immersion-and-invariance scheme for single-input single-output linear systems and a passivity-based scheme for nonlinear systems in observer form are proposed. The proof and interpretation of these results are also based on the notion of active nodes. The simulation results show that the adaptive control schemes proposed in the thesis have superior performance when compared with the classical schemes in the presence of time-varying parameters. Finally, the thesis studies two applications of the theoretical results proposed. The servo control problem for serial elastic actuators, and the disease control problem for interconnected settlements. The discussions show that these problems can be solved efficiently using the framework provided by the thesis.Open Acces

Results on data-driven controllers for unknown nonlinear systems

The big data revolution is deeply changing the way we understand and analyze natural phenomena around us. In the field of control engineering, data-driven control enables researchers to explore new intelligent algorithms to model and control complex dynamical systems. Data-driven control is based on the paradigm of learning controllers of an unknown dynamical system by directly using data. The underlying idea is that information about the model can be gathered from experiments, bypassing completely the identification step, which can be impractical or too costly. This thesis presents data-driven control solutions for different families of unknown dynamical systems, with a focus on both linear and special classes of nonlinear ones. In the first part of the thesis, we consider the linear quadratic regulator problem for linear time-invariant discrete-time systems. The system is assumed to be unknown and information on the system is given by a finite set of data. This allows determining the optimal control law in one shot, with no intermediate identification step. Secondly, we present an online algorithm for learning controllers applied to switched linear systems. By collecting data on the fly, the control mechanism can capture any changes in the dynamics of the plant and adapt itself accordingly to achieve stabilization of the running dynamics. Finally, we derive data-driven methods for a more general class of nonlinear systems via nonlinearity cancellation. To this end, we make use of a "dictionary" of nonlinear terms that includes the nonlinearities of the unknown system

Stabilization of cascaded nonlinear systems under sampling and delays

Over the last decades, the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model. Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system