Adaptive sliding mode observers in uncertain chaotic cryptosystems with a relaxed matching condition

We study the performance of adaptive sliding mode observers in chaotic synchronization and communication in the presence of uncertainties. The proposed robust adaptive observer-based synchronization is used for cryptography based on chaotic masking modulation (CM). Uncertainties are intentionally injected into the chaotic dynamical system to achieve higher security and we use robust sliding mode observer design methods for the uncertain nonlinear dynamics. In addition, a relaxed matching condition is introduced to realize the robust observer design. Finally, a Lorenz system is employed as an illustrative example to demonstrate the effectiveness and feasibility of the proposed cryptosyste

Robust output synchronization for complex nonlinear systems.

Zhao, Jin.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 79-83).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Synchronization of Master-slave Systems --- p.1Chapter 1.2 --- Output Regulation --- p.2Chapter 1.3 --- Typical Nonlinear Systems --- p.4Chapter 1.4 --- Organization --- p.4Chapter 2 --- Synchronization of Chua's Circuit and Van der Pol Oscillator via Inter- nal Model Approach --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- Problem Formulation --- p.8Chapter 2.3 --- Preliminaries --- p.10Chapter 2.4 --- Solvability of the Problem --- p.13Chapter 2.4.1 --- The solution of the regulator equations --- p.14Chapter 2.4.2 --- Steady-state generator --- p.15Chapter 2.4.3 --- Internal model --- p.19Chapter 2.4.4 --- Stabilization --- p.20Chapter 2.4.5 --- Simulation --- p.22Chapter 2.5 --- Conclusions --- p.27Chapter 3 --- Robust Output Regulation of Output Feedback Systems with Nonlinear Exosystems --- p.28Chapter 3.1 --- Introduction --- p.28Chapter 3.2 --- Assumptions and Preliminaries --- p.29Chapter 3.3 --- Solvability of the Synchronization Problem --- p.33Chapter 3.4 --- Comparing Two Approaches for Output Regulation --- p.42Chapter 3.4.1 --- Differences between the two approaches for the output regulation problem --- p.42Chapter 3.4.2 --- Solvability of the regulator equations --- p.43Chapter 3.4.3 --- Solvability of stabilization --- p.47Chapter 3.5 --- Conclusions --- p.49Chapter 4 --- Applications of Robust Regional Synchronization via Output Regulation Techniques --- p.50Chapter 4.1 --- Problem Formulation --- p.50Chapter 4.2 --- Duffing Oscillator Synchronizes with Chua's Circuit --- p.51Chapter 4.2.1 --- Transfer the synchronization problem into the stabilization problem --- p.53Chapter 4.2.2 --- Boundedness of Chua's circuit --- p.57Chapter 4.2.3 --- Stabilization --- p.59Chapter 4.2.4 --- Simulation Results --- p.64Chapter 4.3 --- The Chaotic SMIB Power System Synchronizes with Van der Pol Oscillator --- p.64Chapter 4.3.1 --- Transfer the synchronization problem into the stabilization problem --- p.68Chapter 4.3.2 --- Stabilization --- p.71Chapter 4.3.3 --- Simulation Results --- p.74Chapter 4.4 --- Conclusions --- p.76Chapter 5 --- Conclusions --- p.77Bibliography --- p.7

Learning-based Predictive Control for Nonlinear Systems with Unknown Dynamics Subject to Safety Constraints

Model predictive control (MPC) has been widely employed as an effective method for model-based constrained control. For systems with unknown dynamics, reinforcement learning (RL) and adaptive dynamic programming (ADP) have received notable attention to solve the adaptive optimal control problems. Recently, works on the use of RL in the framework of MPC have emerged, which can enhance the ability of MPC for data-driven control. However, the safety under state constraints and the closed-loop robustness are difficult to be verified due to approximation errors of RL with function approximation structures. Aiming at the above problem, we propose a data-driven robust MPC solution based on incremental RL, called data-driven robust learning-based predictive control (dr-LPC), for perturbed unknown nonlinear systems subject to safety constraints. A data-driven robust MPC (dr-MPC) is firstly formulated with a learned predictor. The incremental Dual Heuristic Programming (DHP) algorithm using an actor-critic architecture is then utilized to solve the online optimization problem of dr-MPC. In each prediction horizon, the actor and critic learn time-varying laws for approximating the optimal control policy and costate respectively, which is different from classical MPCs. The state and control constraints are enforced in the learning process via building a Hamilton-Jacobi-Bellman (HJB) equation and a regularized actor-critic learning structure using logarithmic barrier functions. The closed-loop robustness and safety of the dr-LPC are proven under function approximation errors. Simulation results on two control examples have been reported, which show that the dr-LPC can outperform the DHP and dr-MPC in terms of state regulation, and its average computational time is much smaller than that with the dr-MPC in both examples.Comment: The paper has been submitted at a IEEE Journal for possible publicatio

Control of stochastic chaos using sliding mode method

AbstractStabilizing unstable periodic orbits of a deterministic chaotic system which is perturbed by a stochastic process is studied in this paper. The stochastic chaos is modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of a Wiener process which eventually generates an Ito differential equation. It is also assumed that the chaotic system being studied has some model uncertainties which are not random. The sliding mode controller with some modifications is used for stochastic chaos suppression. It is shown that the system states converge to the desired orbit in such a way that the error covariance converges to an arbitrarily small bound around zero. As some case studies, the stabilization of 1-cycle and 2-cycle orbits of chaotic Duffing and Φ6 Van der Pol systems is investigated by applying the proposed method to their corresponding stochastically perturbed systems. Simulation results show the effectiveness of the method and the accuracy of the statements proved in the paper

Dynamics of Oscillators Coupled by a Medium with Adaptive Impact

In this article we study the dynamics of coupled oscillators. We use mechanical metronomes that are placed over a rigid base. The base moves by a motor in a one-dimensional direction and the movements of the base follow some functions of the phases of the metronomes (in other words, it is controlled to move according to a provided function). Because of the motor and the feedback, the phases of the metronomes affect the movements of the base while on the other hand, when the base moves, it affects the phases of the metronomes in return. For a simple function for the base movement (such as $y = \gamma_{x} [r \theta_1 + (1 - r) \theta_2]$ in which $y$ is the velocity of the base, $\gamma_{x}$ is a multiplier, $r$ is a proportion and $\theta_1$ and $\theta_2$ are phases of the metronomes), we show the effects on the dynamics of the oscillators. Then we study how this function changes in time when its parameters adapt by a feedback. By numerical simulations and experimental tests, we show that the dynamic of the set of oscillators and the base tends to evolve towards a certain region. This region is close to a transition in dynamics of the oscillators; where more frequencies start to appear in the frequency spectra of the phases of the metronomes

Design of Sliding Mode PID Controller with Improved reaching laws for Nonlinear Systems

In this thesis, advanced design technique in sliding mode control (SMC) is presented with focus on PID (Proportional-Integral-Derivative) type Sliding surfaces based Sliding mode control with improved power rate exponential reaching law for Non-linear systems using Modified Particle Swarm Optimization (MPSO). To handle large non-linearities directly, sliding mode controller based on PID-type sliding surface has been designed in this work, where Integral term ensures fast finite convergence time. The controller parameter for various modified structures can be estimated using Modified PSO, which is used as an offline optimization technique. Various reaching law were implemented leading to the proposed improved exponential power rate reaching law, which also improves the finite convergence time. To implement the proposed algorithm, nonlinear mathematical model has to be decrypted without linearizing, and used for the simulation purposes. Their performance is studied using simulations to prove the proposed behavior. The problem of chattering has been overcome by using boundary method and also second order sliding mode method. PI-type sliding surface based second order sliding mode controller with PD surface based SMC compensation is also proposed and implemented. The proposed algorithms have been analyzed using Lyapunov stability criteria. The robustness of the method is provided using simulation results including disturbance and 10% variation in system parameters. Finally process control based hardware is implemented (conical tank system)