Ultimate state boundedness of underactuated spacecraft subject to an unmatched disturbance

Ultimate state boundedness for underactuated spacecraft subject to large non-matched disturbances is attained. First, non-smooth time-invariant state feedback control laws that make the origin asymptotically stable are obtained. Then, the controller is extended to make the closed-loop system globally uniformly ultimately bounded under the following conditions: 1) the disturbances acting on the directly actuated states are known and 2) the disturbance acting on the unactuated state is bounded and its profile need not be known. Finally, numerical simulations are presented to verify the analytical results. A large step disturbance is considered, and it is shown that the proposed controller makes the closed-loop system globally uniformly ultimately bounded. The proposed method is rather general and can be extended to other systems

Stabilizing control design of a motorcycle

This thesis solves the stabilizing control of an autonomous motorcycle. The control of an autonomous motorcycle is a challenging and interesting problem in the field because the plant is under-actuated, unstable and nonlinear. Two major problems that have not been considered in the literature are explicitly solved in our work: (i) the robust control problem of the plant subject to uncertainty and exogenous disturbance; (ii) the non-local stabilization of the nonlinear plant. To achieve the first goal, we propose a robust H_infty controller based on the linearized system, which provides a significant improvement in dealing model uncertainty and disturbance attenuation in comparison with those controllers given by classical linear design tools. To achieve the second goal, we propose a nonlinear controller based on the combination of a nonlinear forwarding method with several other methods for the nonlinear plant through identifying an appropriate upper triangular structure of the nonlinear system. This yields a stability region, the whole upper space above the level ground, such that the trajectory starting from any position in the upper hemi-sphere with arbitrary initial velocities converges to the upright position. Both results are novel and first results of their kinds in control of an autonomous motorcycle. Computer simulations verify the effectiveness of the proposed controllers

Nonlinear Robust Neural Control with Applications to Aerospace Vehicles

Nonlinear control has become increasingly more used over the last few decades, mainly due to the research and development of better analysis tools, that can simulate real-world problems, which are almost always, nonlinear. Nonlinear controllers have the advantage of being more accurate and efficient when dealing with complex scenarios, such as orbit control, satellite rendezvous, or attitude control, compared to linear ones. However, common nonlinear control techniques require having a high-fidelity model, which is often not the case, thereby limiting their use. Additionally, rapid advancements in the field of machine learning have raised the possibility of using tools like neural networks to learn the dynamics of nonlinear systems in an effort to compute control inputs without the need to solve the highly complex mathematical equations that some nonlinear controllers require to solve, in real-time, therefore bypassing the need of higher computational power, which can reduce costs and weight, in space missions. This dissertation will focus on the development of a neural controller based on H8 pseudolinear control, to be applied to the satellite attitude control problem, as well as the satellite orbit control problem. The resulting controller is proven to be robust when dealing with important disturbances that are relevant in space missions, due to being trained using H8 controller data. Moreover, since the original controller is pseudolinear, the neural controller can capture the nonlinearities that exist in the equations of motion as well as in the attitude dynamics equations.Nas últimas décadas, o controlo não-linear tem sido cada vez mais utilizado, maioritariamente devido ao desenvolvimento de melhores ferramentas de análise, utilizadas para a simulação problemas reais, que tendem a ser não-lineares. Os controladores não-lineares têm a vantagem de serem mais precisos e eficientes quando utilizados em situações complexas, como controlo orbital, rendezvous de satélites, e controlo de atitude, comparados com controladores lineares. No entanto, as técnicas comuns de controlo não-linear requerem o uso de modelos com alto grau de fidelidade, o que muitas vezes não é o caso, limitando assim a sua utilização. Além disso, os rápidos avanços no campo de machine learning levantaram a possibilidade de utilizar ferramentas como redes neuronais para aprender a dinâmica de sistemas não lineares, numa tentativa de poder computar as entradas de controlo sem a necessidade de resolver as equações matemáticas altamente complexas que alguns controladores não lineares necessitam que sejam resolvidas, em tempo real, contornando assim a necessidade de maior potência computacional, que pode reduzir custos e peso, em missões espaciais. Esta dissertação focar-se-á no desenvolvimento de um controlador neuronal, baseado em controlo pseudolinear por H8, com o intuito de ser aplicado no problema de controlo orbital, bem como no problema de controlo de atitude. O controlador resultante provou ser robusto ao lidar com perturbações importantes, relevantes em missões espaciais, devido ao facto de ter sido treinado usando dados do controlador H8. Além disso, como o controlador original é pseudolinear, o controlador neuronal pode captar as dinâmicas não lineares que existem nas equações de movimento, bem como nas equações da dinâmica de atitude

Robust stabilization & regulation of nonlinear systems in feed forward form

Zhu Minghui.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references (leaves 144-149).Abstracts in English and Chinese.Abstract --- p.vChapter 1 --- Introduction --- p.1Chapter 1.1 --- Small Gain Theorem --- p.1Chapter 1.2 --- Stabilization for Feedforward Systems --- p.2Chapter 1.3 --- Output Regulation for Feedforward Systems --- p.4Chapter 1.4 --- Organization and Contributions --- p.5Chapter 2 --- Input-to-State Stability for Nonlinear Systems --- p.7Chapter 3 --- Small Gain Theorem with Restrictions for Uncertain Time-varying Non- linear Systems --- p.13Chapter 3.1 --- Input-to-State Stability Small Gain Theorem with Restrictions for Uncer- tain Nonlinear Time-varying Systems --- p.14Chapter 3.1.1 --- Nonlinear Time Invariant Systems Case --- p.14Chapter 3.1.2 --- Uncertain Time-varying Nonlinear Systems Case --- p.16Chapter 3.1.3 --- Remarks and Corollaries --- p.28Chapter 3.2 --- Semi-Uniform Input-to-State Stability Small Gain Theorem with Restric- tions for Uncertain Nonlinear Time-varying Systems --- p.38Chapter 3.3 --- Asymptotic Small Gain Theorem with Restrictions for Uncertain Nonlinear Time-varying Systems --- p.44Chapter 3.4 --- Input-to-State Stability Small Gain Theorem with Restrictions for Uncer- tain Time-varying Systems of Functional Differential Equations --- p.49Chapter 4 --- A Remark on Various Small Gain Conditions --- p.52Chapter 4.1 --- Introduction --- p.52Chapter 4.2 --- Preliminary --- p.53Chapter 4.3 --- The Sufficient and Necessary Condition for Input-to-State Stability of Time-varying Systems --- p.56Chapter 4.3.1 --- ISS-Lyapunov functions for Time-varying Systems --- p.56Chapter 4.3.2 --- A Remark on Input-to-State Stability for Time-varying Systems --- p.61Chapter 4.4 --- Comparison of Various Small Gain Theorems --- p.63Chapter 4.4.1 --- Comparison of Theorem 4.1 and Theorem 4.2 --- p.63Chapter 4.4.2 --- "Comparison of Theorem 4.1 and Theorem 4.3, Theorem 4.2 and Theorem 4.3" --- p.68Chapter 4.5 --- Two Small Gain Theorems for Time-varying Systems --- p.70Chapter 4.6 --- Conclusion --- p.73Chapter 5 --- Semi-global Robust Stabilization for A Class of Feedforward Systems --- p.74Chapter 5.1 --- Introduction --- p.74Chapter 5.2 --- Main result --- p.76Chapter 5.3 --- Conclusion --- p.91Chapter 6 --- Global Robust Stabilization for A Class of Feedforward Systems --- p.93Chapter 6.1 --- Main Result --- p.93Chapter 6.2 --- Conclusion --- p.104Chapter 7 --- Global Robust Stabilization and Output Regulation for A Class of Feedforward Systems --- p.105Chapter 7.1 --- Introduction --- p.105Chapter 7.2 --- Preliminary --- p.107Chapter 7.3 --- Global Robust Stabilization via Partial State Feedback --- p.108Chapter 7.3.1 --- RAG with restrictions --- p.110Chapter 7.3.2 --- Fulfillment of the restrictions --- p.114Chapter 7.3.3 --- Small gain conditions --- p.117Chapter 7.3.4 --- Uniform Global Asymptotic Stability of Closed Loop System . . . . --- p.118Chapter 7.4 --- Global Robust Output Regulation --- p.118Chapter 7.5 --- Conclusion --- p.134Chapter 8 --- Conclusion --- p.136Chapter A --- Appendix --- p.138List of Figures --- p.143Bibliography --- p.144Biography --- p.15

Nonlinear Tracking Control Using a Robust Differential-Algebraic Approach.

This dissertation presents the development and application of an inherently robust nonlinear trajectory tracking control design methodology which is based on linearization along a nominal trajectory. The problem of trajectory tracking is reduced to two separate control problems. The first is to compute the nominal control signal that is needed to place a nonlinear system on a desired trajectory. The second problem is one of stabilizing the nominal trajectory. The primary development of this work is the development of practical methods for designing error regulators for Linear Time Varying systems, which allows for the application of trajectory linearization to time varying trajectories for nonlinear systems. This development is based on a new Differential Algebraic Spectral Theory. The problem of robust tracking for nonlinear systems with parametric uncertainty is studied in relation to the Linear Time Varying spectrum. The control method presented herein constitutes a rather general control strategy for nonlinear dynamic systems. Design and simulation case studies for some challenging nonlinear tracking problems are considered. These control problems include: two academic problems, a pitch autopilot design for a skid-to-turn missile, a two link robot controller, a four degree of freedom roll-yaw autopilot, and a complete six degree of freedom Bank-to-turn planar missile autopilot. The simulation results for these designs show significant improvements in performance and robustness compared to other current control strategies

Exponential Stabilization of Driftless Nonlinear Control Systems

This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, xdot = X1(x)u1 + .... + Xm(x)um, x ∈ ℝ^n Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a non-standard dilation. Even though the approximation can be given a coordinate-free interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the closed-loop system. The stability achieved is called p-exponential stability. The closed-loop system is stable and the equilibrium point is exponentially attractive. This extended notion of exponential stability is required since the feedback, and hence the closed-loop system, is not Lipschitz. However, it is shown that the convergence rate of a Lipschitz closed-loop driftless system cannot be bounded by an exponential envelope. The synthesis methods generate feedbacks which are smooth on ℝ^n \ {0}. The solutions of the closed-loop system are proven to be unique in this case. In addition, the control inputs for many driftless systems are velocities. For this class of systems it is more appropriate for the control law to specify actuator forces instead of velocities. We have extended the kinematic velocity controllers to controllers which command forces and still p-exponentially stabilize the system. Perhaps the ultimate justification of the methods proposed in this thesis are the experimental results. The experiments demonstrate the superior convergence performance of the p-exponential stabilizers versus traditional smooth feedbacks. The experiments also highlight the importance of transformation conditioning in the feedbacks. Other design issues, such as scaling the measured states to eliminate hunting, are discussed. The methods in this thesis bring the practical control of strongly nonlinear systems one step closer

Control Of Nonh=holonomic Systems

Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles\u27 kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs

Optimal control with structure constraints and its application to the design of passive mechanical systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Page 214 blank.Includes bibliographical references.Structured control (static output feedback, reduced-order control, and decentralized feedback) is one of the most important open problems in control theory and practice. In this thesis, various techniques for synthesis of structured controllers are surveyed and investigated, including H2 optimization, H[infinity] optimization, L1 control, eigenvalue and eigenstructure treatment, and multiobjective control. Unstructured control-full- state feedback and full-order control-is also discussed. Riccati-based synthesis, linear matrix inequalities (LMI), homotopy methods, gradient- and subgradientbased optimization are used. Some new algorithms and extensions are proposed, such as a subgradient-based method to maximize the minimal damping with structured feedback, a multiplier method for structured optimal H2 control with pole regional placement, and the LMI-based H2/H[infinity]/pole suboptimal synthesis with static output feedback. Recent advances in related areas are comprehensively surveyed and future research directions are suggested. In this thesis we cast the parameter optimization of passive mechanical systems as a decentralized control problem in state space, so that we can apply various decentralized control techniques to the parameter design which might be very hard traditionally. More practical constraints for mechanical system design are considered; for example, the parameters are restricted to be nonnegative, symmetric, or within some physically-achievable ranges. Marginally statable systems and hysterically damped systems are also discussed. Numerical examples and experimental results are given to illustrate the successful application of decentralized control techniques to the design of passive mechanical systems, such as multi-degree-of-freedom tuned-mass dampers, passive vehicle suspensions, and others.by Lei Zuo.S.M

Development of U-model enhansed nonlinear systems

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu’s Doctoral thesis, and U-model approach was firstly published in the journal paper titled with ‘U-model based pole placement for nonlinear plants’ in 2002.The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches.Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems.This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure.With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches.The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm.A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods