Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

Nonlinear Control Strategies for Cooperative Control of Multi-Robot Systems

This thesis deals with distributed control strategies for cooperative control of multi-robot systems. Specifically, distributed coordination strategies are presented for groups of mobile robots. The formation control problem is initially solved exploiting artificial potential fields. The purpose of the presented formation control algorithm is to drive a group of mobile robots to create a completely arbitrarily shaped formation. Robots are initially controlled to create a regular polygon formation. A bijective coordinate transformation is then exploited to extend the scope of this strategy, to obtain arbitrarily shaped formations. For this purpose, artificial potential fields are specifically designed, and robots are driven to follow their negative gradient. Artificial potential fields are then subsequently exploited to solve the coordinated path tracking problem, thus making the robots autonomously spread along predefined paths, and move along them in a coordinated way. Formation control problem is then solved exploiting a consensus based approach. Specifically, weighted graphs are used both to define the desired formation, and to implement collision avoidance. As expected for consensus based algorithms, this control strategy is experimentally shown to be robust to the presence of communication delays. The global connectivity maintenance issue is then considered. Specifically, an estimation procedure is introduced to allow each agent to compute its own estimate of the algebraic connectivity of the communication graph, in a distributed manner. This estimate is then exploited to develop a gradient based control strategy that ensures that the communication graph remains connected, as the system evolves. The proposed control strategy is developed initially for single-integrator kinematic agents, and is then extended to Lagrangian dynamical systems.

Improved robust control of nonlinear stochastic systems using uncertain models

We introduce a technique for quantifying and then exploiting uncertainty in nonlinear stochastic control systems. The approach is suboptimal though robust and relies upon the approximation of the forward and inverse plant models by neural networks, which also estimate the intrinsic uncertainty. Sampling from the resulting Gaussian distributions of the inversion based neurocontroller allows us to introduce a control law which is demonstrably more robust than traditional adaptive controllers.

Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

We introduce a novel inversion-based neuro-controller for solving control problems involving uncertain nonlinear systems that could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

On the motion planning & control of nonlinear robotic systems

In the last decades, we saw a soaring interest in autonomous robots boosted not only by academia and industry, but also by the ever in- creasing demand from civil users. As a matter of fact, autonomous robots are fast spreading in all aspects of human life, we can see them clean houses, navigate through city traffic, or harvest fruits and vegetables. Almost all commercial drones already exhibit unprecedented and sophisticated skills which makes them suitable for these applications, such as obstacle avoidance, simultaneous localisation and mapping, path planning, visual-inertial odometry, and object tracking. The major limitations of such robotic platforms lie in the limited payload that can carry, in their costs, and in the limited autonomy due to finite battery capability. For this reason researchers start to develop new algorithms able to run even on resource constrained platforms both in terms of computation capabilities and limited types of endowed sensors, focusing especially on very cheap sensors and hardware. The possibility to use a limited number of sensors allowed to scale a lot the UAVs size, while the implementation of new efficient algorithms, performing the same task in lower time, allows for lower autonomy. However, the developed robots are not mature enough to completely operate autonomously without human supervision due to still too big dimensions (especially for aerial vehicles), which make these platforms unsafe for humans, and the high probability of numerical, and decision, errors that robots may make. In this perspective, this thesis aims to review and improve the current state-of-the-art solutions for autonomous navigation from a purely practical point of view. In particular, we deeply focused on the problems of robot control, trajectory planning, environments exploration, and obstacle avoidance.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.

Constraint satisfaction techniques under uncertain conditions for fault diagnosis in nonlinear dynamic systems

The speed of fault isolation is crucial for the design and reconfiguration of fault tolerant control (FTC). In this paper the fault isolation problem is stated as a constraint satisfaction problem (CSP) and solved using constraint propagation techniques. The proposed method is based on constraint satisfaction techniques and uncertainty space refining of interval parameters. In comparison with other approaches based on adaptive observers, the major advantage of the presented method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements and model errors and without the monotonicity assumption. In order to illustrate the proposed approach, a case study of a nonlinear dynamic system is presented

Constraint satisfaction techniques under uncertain conditions for fault diagnosis in nonlinear dynamic systems

The speed of fault isolation is crucial for the design and reconfiguration of fault tolerant control (FTC). In this paper the fault isolation problem is stated as a constraint satisfaction problem (CSP) and solved using constraint propagation techniques. The proposed method is based on constraint satisfaction techniques and uncertainty space refining of interval parameters. In comparison with other approaches based on adaptive observers, the major advantage of the presented method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements and model errors and without the monotonicity assumption. In order to illustrate the proposed approach, a case study of a nonlinear dynamic system is presented

Fault diagnosis by refining the parameter uncertainty space of nonlinear dynamic systems

This paper deals with fault detection and isolation problems for nonlinear dynamic systems. Both problems are stated as constraint satisfaction problems (CSP) and solved using consistency techniques. The main contribution is the isolation method based on consistency techniques and uncertainty space refining of interval parameters. The major advantage of this method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements, and model errors. Interval calculations bring independence from the assumption of monotony considered by several approaches for fault isolation which are based on observers. An application to a well known alcoholic fermentation process model is presented

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)