The geometry of low-rank Kalman filters

An important property of the Kalman filter is that the underlying Riccati flow is a contraction for the natural metric of the cone of symmetric positive definite matrices. The present paper studies the geometry of a low-rank version of the Kalman filter. The underlying Riccati flow evolves on the manifold of fixed rank symmetric positive semidefinite matrices. Contraction properties of the low-rank flow are studied by means of a suitable metric recently introduced by the authors.Comment: Final version published in Matrix Information Geometry, pp53-68, Springer Verlag, 201

A Supervisor for Control of Mode-switch Process

Many processes operate only around a limited number of operation points. In order to have adequate control around each operation point, and adaptive controller could be used. When the operation point changes often, a large number of parameters would have to be adapted over and over again. This makes application of conventional adaptive control unattractive, which is more suited for processes with slowly changing parameters. Furthermore, continuous adaptation is not always needed or desired. An extension of adaptive control is presented, in which for each operation point the process behaviour can be stored in a memory, retrieved from it and evaluated. These functions are co-ordinated by a ¿supervisor¿. This concept is referred to as a supervisor for control of mode-switch processes. It leads to an adaptive control structure which quickly adjusts the controller parameters based on retrieval of old information, without the need to fully relearn each time. This approach has been tested on experimental set-ups of a flexible beam and of a flexible two-link robot arm, but it is directly applicable to other processes, for instance, in the (petro) chemical industry

Event-Based {LQR} with Integral Action

International audienceIn this paper, a state-feedback linear-quadratic regulator (LQR) is proposed for event-based control of a linear system. An interesting property of LQRs is that an optimal response of the system can be obtained in accordance to some specifications, like the actuator limits. An integral action is also added in order to not only restrict the study to null stabilization but also to tracking. The idea is to consider an external control loop and stabilize the integral of the error between the measurement and a desired setpoint to track. However, an event-triggered integral can lead to important overshoots when the interval between two successive events becomes large. Therefore, an exponential forgetting factor of the sampling interval is proposed as a solution to avoid such problems. The whole proposal is tested on a real-time system (a gyroscope) in order to highlight its ability, the reduction of control updates and the respect to the actuator limits

Short-term memory for pictures seen once or twice

The present study is concerned with the effects of exposure time, repetition, spacing and lag on old/new recognition memory for generic visual scenes presented in a RSVP paradigm. Early memory studies with verbal material found that knowledge of total exposure time at study is sufficient to accurately predict memory performance at test (the Total Time Hypothesis), irrespective of number of repetitions, spacing or lag. However, other studies have disputed such simple dependence of memory strength on total study time, demonstrating super-additive facilitatory effects of spacing and lag, as well as inhibitory effects, such as the Ranschburg effect, Repetition Blindness and the Attentional Blink. In the experimental conditions of the present study we find no evidence of either facilitatory or inhibitory effects: recognition memory for pictures in RSVP supports the Total Time Hypothesis. The data are consistent with an Unequal-Variance Signal Detection Theory model of memory that assumes the average strength and the variance of the familiarity of pictures both increase with total study time. The main conclusion is that the growth of visual scene familiarity with temporal exposure and repetition is a stochastically independent process

Continual Learning-Based Optimal Output Tracking of Nonlinear Discrete-Time Systems with Constraints: Application to Safe Cargo Transfer

This Paper Addresses a Novel Lifelong Learning (LL)-Based Optimal Output Tracking Control of Uncertain Non-Linear Affine Discrete-Time Systems (DT) with State Constraints. First, to Deal with Optimal Tracking and Reduce the Steady State Error, a Novel Augmented System, Including Tracking Error and its Integral Value and Desired Trajectory, is Proposed. to Guarantee Safety, an Asymmetric Barrier Function (BF) is Incorporated into the Utility Function to Keep the Tracking Error in a Safe Region. Then, an Adaptive Neural Network (NN) Observer is Employed to Estimate the State Vector and the Control Input Matrix of the Uncertain Nonlinear System. Next, an NN-Based Actor-Critic Framework is Utilized to Estimate the Optimal Control Input and the Value Function by using the Estimated State Vector and Control Coefficient Matrix. to Achieve LL for a Multitask Environment in Order to Avoid the Catastrophic Forgetting Issue, the Exponential Weight Velocity Attenuation (EWVA) Scheme is Integrated into the Critic Update Law. Finally, the Proposed Tracker is Applied to a Safe Cargo/ Crew Transfer from a Large Cargo Ship to a Lighter Surface Effect Ship (SES) in Severe Sea Conditions

A Model-Free Control System Based on the Sliding Mode Control with Automatic Tuning Using as On-Line Parameter Estimation Approach

The sliding mode control algorithm and Lyapunov-based methods, have received much attention recently due to their ability to directly handle nonlinear systems while guaranteeing closed-loop tracking stability. In this work, a unique model-free sliding mode control technique has developed solely based on previous control inputs. The new method requires only knowledge of the system order and state measurements and does not require a theoretical model of the dynamic system. Lyapunov’s stability theorem is used in the controller formulation process to ensure closed-loop asymptotic stability. High frequency chattering of the control effort is reduced by using a smoothing boundary layer into the control law. Parameters variation during control operating and noise effect cannot be handled by the model-free controller if the controller tuning parameters are chosen arbitrarily since tracking performance becomes unacceptable. In addition, in previous work, the bounds of the input influence gain parameters were assumed to be known to derive the model-free controller. Therefore, in this work, a new approach is proposed for estimating the increment to the switching gain in real-time to ensure the sliding condition (which guarantees closed-loop tracking stability) is satisfied using a control law form that assumes a strictly unitary input influence gain. In formulation of estimation law, an exponential forgetting factor is combined with the least-squares estimator to ensure the updated data are used and past data are excluded. An automatic bounded forgetting tuning technique is developed to maintain the benefits of data forgetting while avoiding the possibility of gain unboundedness in absence of persistent excitation. The tuning estimator is assured that the resulting gain matrix is upper bounded regardless of the persistent excitation by suspending the data forgetting if the gain matrix reaches the specified upper bound. Simulations are performed on a series of linear and nonlinear SISO and MIMO systems with and without including actuator time-delay effects. Finally, a model is developed to simulate a quadcopter as a real-world application case. In all cases, the controller achieved perfect or near-perfect tracking performance using updated controller and on-line estimator tuning process