Reverse Engineering Biological Control Systems for Applications in Process Control.

The main emphasis of this dissertation is the development of nonlinear control strategies based on biological control systems. Commonly utilized biological control schemes have been studied in order to reverse engineer the important concepts for applications in process control. This approach has led to the development of a nonlinear habituating control strategy and nonlinear model reference adaptive control schemes. Habituating control is a controller design strategy for nonlinear systems with more manipulated inputs than controlled outputs. Nonlinear control laws that provide input-output linearization while simultaneously minimizing the cost of affecting control are derived. Local stability analysis shows the controller can provide a simple solution to singularity and non-minimum phase problems. A direct adaptive control strategy for a class of single-input, single-output non-linear systems is presented. The major advantage is that a detailed dynamic non-linear model is not required for controller design. Unknown controller functions in the associated input-output linearizing control law are approximated using locally supported radial basis functions. Lyapunov stability analysis is used to derive parameter update laws which ensure the state vector remains bounded and the plant output asymptotically tracks the output of a linear reference model. A nonlinear model reference adaptive control strategy in which a linear model (or multiple linear models) is embedded within the nonlinear controller is presented. The nonlinear control law is constructed by embedding linear controller gains derived from models obtained using standard linear system identification techniques within the associated input-output linearizing control law. Higher-order controller functions are approximated with radial basis functions. Lyapunov stability analysis is used to derive stable parameter update laws. The major disadvantage of the previous techniques is computational expense. Two modifications have been developed. First, the effective dimension is reduced by applying nonlinear principal component analysis to the state variable data obtained from open-loop tests. This allows basis functions to be placed in a lower dimensional space than the original state space. Second, the total number of basis functions is fixed a priori and an algorithm which adds/prunes basis function centers to surround the current operating point on-line is utilized

Adaptive control using variable structure systems.

Adaptive control is employed in control systems required to operate satisfactorily regardless of parameter variations, external disturbances and changes in the environment. A conceptually simple approach to adaptive control is the model reference approach which yields a nonlinear feedback system. In a model reference control system the system output is made to follow the output of a specified model. There are numerous approaches to the design of model reference adaptive control systems (MRAC). In this thesis the theory of variable structure systems (VSS) is studied and applied in the design of MRAC systems. VSS are inherently nonlinear feedback systems which exhibit certain adaptive properties including insensitivity to a range of parameter variations and certain external disturbances when operating in the sliding mode. The application of VSS theory to the problem of adaptive model-following has demonstrated the simplicity of the design. It also ensures the asymptotic stability of the controlled system and provides direct control over the error transient. The notion of system zeros arises naturally when tackling the problem of output model-following control systems. Certain interrelations between VSS, system zeros and the output model following problem have suggested a new method for computing the zeros of linear multivariable square systems. A fundamental operator in VSS is shown to be a projector. The employment of projector theory in the study of VSS provides further insight into their operation. Furthermore new methods for constructing the switching hyperplanes matrix are formulated by utilizing projector theory. The linear control law ensuring output model-following and the necessary order reduction is shown to be identical to the equivalent control encountered in VSS. The control law also decouples the system, assigns arbitrary poles and possesses certain adaptive properties. The extension of VSS theory to output model following systems using output information is also discussed

The adaptive observer

The simple generation of state from available measurements, for use in systems for which the criteria defining the acceptable state behavior mandates a control that is dependent upon unavailable measurement is described as an adaptive means for determining the state of a linear time invariant differential system having unknown parameters. A single input output adaptive observer and the reduced adaptive observer is developed. The basic ideas for both the adaptive observer and the nonadaptive observer are examined. A survey of the Liapunov synthesis technique is taken, and the technique is applied to adaptive algorithm for the adaptive observer

Neural Network based Direct MRAC Technique for Improving Tracking Performance for Nonlinear Pendulum System

This paper investigates the application of a neural network-based model reference adaptive intelligent controller for controlling the nonlinear systems. The idea is to control the plant by minimizing the tracking error between the desired reference model and the nonlinear system using conventional model reference adaptive con-troller by estimating the adaptation law using a multilayer backpropagation neural network. In the conventional model reference adaptive controller block, the controller is designed to realize the plant output converges to reference model output based on the plant, which is linear. This controller is effective for controlling the linear plant with unknown parameters. However, controlling of a nonlinear system using MRAC in real-time is difficult. The Neural Network is used to compensate the nonlinearity and disturbance of the nonlinear pendulum that is not taken into consideration in the conventional MRAC therefore, the proposed paper can significantly improve the system behaviour and force the system to behave the reference model and reduce the error between the model and the plant output. Adaptive law using Lyapunov stability criteria for updating the controller parameters online has been formulated. The behaviour of the proposed control scheme is verified by developing the simula-tion results for a simple pendulum. It is shown that the proposed neural net-work-based Direct MRAC has small rising time, steady-state error and settling time for a different disturbance than Conventional Direct MRAC adaptive control

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

This paper presents a new method of synthesizing an output feedback adaptive controller for a class of uncertain, non-square, multi-input multi-output systems that often occur in hypersonic vehicle models. The main challenge that needs to be addressed is the determination of a corresponding square and strictly positive real transfer function. This paper proposes a new procedure to synthesize two gain matrices that allows the realization of such a transfer function, thereby allowing a globally stable adaptive output feedback law to be generated. The unique features of this output feedback adaptive controller are a baseline controller that uses a Luenberger observer, a closed-loop reference model, manipulations of a bilinear matrix inequality, and the Kalman-Yakubovich Lemma. Using these features, a simple design procedure is proposed for the adaptive controller, and the corresponding stability property is established. The proposed adaptive controller is compared to the classical multi-input multi-output adaptive controller. A numerical example based on a scramjet powered, blended wing-body generic hypersonic vehicle model is presented. The 6 degree-of-freedom nonlinear vehicle model is linearized, giving the design model for which the controller is synthesized. The adaptive output feedback controller is then applied to an evaluation model, which is nonlinear, coupled, and includes actuator dynamics, and is shown to result in stable tracking in the presence of uncertainties that destabilize the baseline linear output feedback controller.This research is funded by the Air Force Research Laboratory/Aerospace Systems Directorate grant FA 8650-07-2-3744 for the Michigan/MIT/AFRL Collaborative Center in Control Sciences and the Boeing Strategic University Initiative. Approved for Public Release; Distribution Unlimited. Case Number 88ABW- 2014-2551

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

Feedback Linearization of Nonlinear Systems: Robustness and Adaptive Control.

Feedback linearization provides an effective means of designing nonlinear control systems. This method permits one to have an exactly equivalent linear system by using a coordinate transformation and state feedback. Once the nonlinear system is transformed to a linear system, one can proceed with well developed control technologies for linear systems. Feedback linearization is based on a model of the real system. If there is mismatch between the model and the real plant, feedback linearization does not yield an exactly linear system. The question of robustness then arises: will a controller based on the model be stable when applied to the real plant? We have developed a theoretical approach to analyze robustness of feedback linearization of SISO (Single-Input Single-Output) systems. We have also considered the dimensional reduction of a high dimensional model which is not a standard singularly perturbed system. Specifically we have found sufficient conditions for boundedness and convergence of the system trajectories when feedback linearization based on a nominal mathematical model is applied to an uncertain real plant which may have parametric and structural uncertainties as well as unmodeled dynamics. The developed approach does not require the restrictive conditions which are commonly used in the previously developed methods of robustness analysis. Furthermore, for parametric uncertainties a nonlinear adaptive control of feedback linearizable processes is proposed. The main feature of the proposed nonlinear adaptive control system is that it is relatively straightforward and simple. For this adaptive control system we have found sufficient conditions for stability of the output regulation and tracking of feedback linearizable systems using the second method of Lyapunov. Examples of the robustness analysis and the adaptive control for unstable chemical and biochemical reactors are given

Meta-Learning-Based Robust Adaptive Flight Control Under Uncertain Wind Conditions

Realtime model learning proves challenging for complex dynamical systems, such as drones flying in variable wind conditions. Machine learning technique such as deep neural networks have high representation power but is often too slow to update onboard. On the other hand, adaptive control relies on simple linear parameter models can update as fast as the feedback control loop. We propose an online composite adaptation method that treats outputs from a deep neural network as a set of basis functions capable of representing different wind conditions. To help with training, meta-learning techniques are used to optimize the network output useful for adaptation. We validate our approach by flying a drone in an open air wind tunnel under varying wind conditions and along challenging trajectories. We compare the result with other adaptive controller with different basis function sets and show improvement over tracking and prediction errors.Comment: This article presents preliminary results and will be update

Adaptive λ-[lambda]-tracking for a class of infinite-dimensional systems

For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius lambda>0. This control strategy, called lambda-tracking, combines proportional error feedback with a simple nonlinear adaptation of the feedback gain. It does not involve any parameter estimation algorithms, nor is it based on the internal model principle. The class of reference signals is W1,00, the Sobolev space of absolutely continuous functions which are bounded and have essentially bounded derivative. The control strategy is robust with respect to output measurement noise in W1,00 and bounded input disturbances. We apply our results to retarded systems and integrodifferential systems