This paper deals with an adaptive H∞-control for the Lagrangian systems with the visual feedback in presence of parametric uncertainties. Based on an adaptive manipulator control, the proposed controller consists of the visual PD feedback part and the full dynamics feedforward part with the update law of the parametric uncertainty. The L2-gain performance analysis of the proposed controller is carried out and its asymptotic property is examined. For the L2-gain performance analysis, the image feature parameter potential plays an important role as the storage function.
This paper considers characterization of the set of reference signals which are 'safe' for the systems with pointwise-in-time state and control constraints. The main idea is to construct two certain subsets such that for any reference input which is contained in the subset of the space of reference signals, avoiding constraints violation is equivalent to restricting the initial condition of a closed-loop system to the other subset of the state space. This paper also presents a technique to resolve tracking problems subject to state and control constraints. The method consists of adding to a primal closed-loop system a nonlinear device called a reference governor which manipulates the desired reference signal in order to fulfill the specified constraints. An admissibility condition on the initial state is satisfied and reference signal converges to an admissible region, the control scheme is proved to fulfill the constraints and set-point tracking requirements.
The dynamics of a two-link planer manipulator with a free joint is described by non-linear ordinary differential equations including trigonometric functions. By commanding repetitive tasks, it is estimated that non-linear phenomena including chaotic motions are occurred on the manipulator. In this paper, some dynamical properties are analyzed with bifurcation theories. Moreover, some nonlinear phenomena of the manipulator are investigated with bifurcation diagrams in several parameter planes are calculated using an algorithm based on the geometric approach. In results, by applying a torque to 1st-joint performing repetitive motion, the 2nd-joint of the manipulator exhibits resonant motions, non-resonant motions, rotating motions, and chaotic motions.
The dynamic processes of chaotic neural networks are investigated in the reinforcement adaptation scheme as a simple model of brain-like function. There appears spontaneous transition from a learning phase with slow adjustment to a retrieving phase with fast adjustment under switching inputs. Learning and retrieving can be considered as two aspects of the same dynamical process. In a reinforcement scenario, it is important that there should be some source of fluctuation in the network, so that the space of possible outputs can be explored until a correct output is found. This is well done by using chaotic neurons, not stochastic units.
In this paper we deal with the sampled-data feedback systems with a class of nonlinearities modeled as the parallel connection of a memoryless time-invariant nonlinearity and a dynamical time-varying nonlinearity. We derive a stability criterion for such systems, which includes as special cases the stability criteria of Popov type and circle-criterion type, and which corresponds to the shifted Popov criterion in the continuous-time case. We also show that checking the stability condition of this criterion reduces to a convex problem in the frequency domain.
This paper proposes two efficient methods to design a robust feedback control system by use of neural networks. The first method is based on L2 gain, and two different neural networks are used. The controller is trained to be robust as a result of competition between neural networks. The second method is based on MiniMax optimization, and is useful to treat parametric uncertainties. In both methods, robustness of the neural network can be quantified. It is very easy to combine proposed methods so that effective methods for various problems can be derived.
Yoyo is a simple toy but it has complicated dynamical characteristics. This paper describes a model of the yoyo suitable for feedback control and a visual feedback control scheme based on this model. The validity of the model and the control scheme is evaluated by the simulations and the experiments on PUMA 560.