Constrained Adaptive Control of Nonlinear Systems with Application to Hypersonic Vehicles
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Constraints in input, output, and states are evident in most of the practical systems. Explicitly incorporating these constraints into the control design process leads to its superior performance in general. Therefore, considering different types of constraints, several robust constrained adaptive nonlinear control designs are proposed in this thesis for different classes of uncertain nonlinear. In the first part of this thesis, a barrier Lyapunov function (BLF) based state constrained adaptive control design is presented for two different classes of uncertain nonlinear systems, known as nonlinear systems with relative degree one and Euler-Lagrange systems. In adaptive control synthesis, a neural network-based approximated system dynamics is constructed to approximate the model uncertainties of the system, and then a tracking controller is designed to achieve the desired tracking response. The weights of the neural network are updated using a Lyapunov stable weight update rule. It is shown that the closed-loop states of the system both remain bounded within the imposed constraints as well as asymptotically converge to a predefined domain. In the second part of this thesis, error transformation based state-constrained adaptive control design is proposed for generic second-order nonlinear systems with state and input constraints, model uncertainties, and external disturbances. A new error transformation is proposed to enforce state constraints; Nussbaum gain is used to impose desired input constraints, and radial basis function neural networks (RBFNNs) are utilized to approximate modeling uncertainties. In this control design philosophy, first, imposed constraints are converted into error constraints and then, using the proposed error transformation, the constrained system is transformed into equivalent unconstrained system. Next, a stable adaptive controller is designed for the unconstrained system, which indirectly establishes the stability of the constrained system without violation of imposed constraints. The closed-loop stability of the system is proven using the Lyapunov stability theory. In the third part of this thesis, an adaptive controller is derived for a feedback linearizable MIMO nonlinear system subjected to time-varying output constraints, input constraints, unknown control directions, modeling uncertainties, and external disturbances. In the control design, another novel error transformation is used to enforce time-varying output constraints, and Nussbaum gain is used to handle input constraints and unknown control directions. One of the features of the proposed adaptive controller is that only a single variable is required to approximate the uncertainties of the whole system, consequently minimizing the computational requirement. Another feature of the proposed controller is that zero error tracking is achieved in presence of unstructured uncertainties and external disturbances. The aforementioned control designs are scalable and can be reduced into output-constrained control and unconstrained control by changing the nature of error dependent controller gain matrices. Controllers can also be used to constrain the closed-loop error of the system directly, thereby minimizing error transients. Furthermore, proposed controllers give flexibility to impose independent constraints on the desired component of the system states and lead to easy on-board implementable closed-form control solutions. A two-link robot manipulator problem and other benchmark problems are used to demonstrate the effectiveness of the proposed control designs by performing extensive simulation results. In the last part of this thesis, a real-life application problem is selected, where the objective is to effectively control a hypersonic flight vehicle during its cruise. The problem is quite challenging as it demands narrow bounds on both input and state in the presence of large modeling uncertainties. The control objective is achieved by using the proposed BLF based constrained adaptive controller. A three-loop architecture is proposed to synthesis this adaptive flight controller, which ensures that the vehicle velocity, attitude and angular body rates remain bounded within the prescribed bounds. The proposed adaptive control leads to quick learning of the unknown function in the system dynamics with much lesser transients. It also ensures that the imposed state constraints are not violated at any point of time. Effectiveness of the control design is illustrated by carrying out a large number of Monte-Carlo like randomized high fidelity six-degree-of-freedom (Six-DOF) simulation studies for a winged-cone hypersonic vehicle. The Six-DOF model was constructed by collecting the necessary aerodynamic and inertial data of the vehicle found scattered in various literature and integrating those into the air-frame equations of motion. Simulation results show that the proposed controller is quite robust to effectively control the vehicle in the presence of significant modeling uncertainties.