Computing Dynamic Output Feedback Laws

The pole placement problem asks to find laws to feed the output of a plant governed by a linear system of differential equations back to the input of the plant so that the resulting closed-loop system has a desired set of eigenvalues. Converting this problem into a question of enumerative geometry, efficient numerical homotopy algorithms to solve this problem for general Multi-Input-Multi-Output (MIMO) systems have been proposed recently. While dynamic feedback laws offer a wider range of use, the realization of the output of the numerical homotopies as a machine to control the plant in the time domain has not been addressed before. In this paper we present symbolic-numeric algorithms to turn the solution to the question of enumerative geometry into a useful control feedback machine. We report on numerical experiments with our publicly available software and illustrate its application on various control problems from the literature.Comment: 20 pages, 3 figures; the software described in this paper is publicly available via http://www.math.uic.edu/~jan/download.htm

Adaptive Resonance: An Emerging Neural Theory of Cognition

Adaptive resonance is a theory of cognitive information processing which has been realized as a family of neural network models. In recent years, these models have evolved to incorporate new capabilities in the cognitive, neural, computational, and technological domains. Minimal models provide a conceptual framework, for formulating questions about the nature of cognition; an architectural framework, for mapping cognitive functions to cortical regions; a semantic framework, for precisely defining terms; and a computational framework, for testing hypotheses. These systems are here exemplified by the distributed ART (dART) model, which generalizes localist ART systems to allow arbitrarily distributed code representations, while retaining basic capabilities such as stable fast learning and scalability. Since each component is placed in the context of a unified real-time system, analysis can move from the level of neural processes, including learning laws and rules of synaptic transmission, to cognitive processes, including attention and consciousness. Local design is driven by global functional constraints, with each network synthesizing a dynamic balance of opposing tendencies. The self-contained working ART and dART models can also be transferred to technology, in areas that include remote sensing, sensor fusion, and content-addressable information retrieval from large databases.Office of Naval Research and the defense Advanced Research Projects Agency (N00014-95-1-0409, N00014-1-95-0657); National Institutes of Health (20-316-4304-5

Secure and Private Implementation of Dynamic Controllers Using Semi-Homomorphic Encryption

This paper presents a secure and private implementation of linear time-invariant dynamic controllers using Paillier's encryption, a semi-homomorphic encryption method. To avoid overflow or underflow within the encryption domain, the state of the controller is reset periodically. A control design approach is presented to ensure stability and optimize performance of the closed-loop system with encrypted controller.Comment: Improved numerical exampl

Learning a Structured Neural Network Policy for a Hopping Task

In this work we present a method for learning a reactive policy for a simple dynamic locomotion task involving hard impact and switching contacts where we assume the contact location and contact timing to be unknown. To learn such a policy, we use optimal control to optimize a local controller for a fixed environment and contacts. We learn the contact-rich dynamics for our underactuated systems along these trajectories in a sample efficient manner. We use the optimized policies to learn the reactive policy in form of a neural network. Using a new neural network architecture, we are able to preserve more information from the local policy and make its output interpretable in the sense that its output in terms of desired trajectories, feedforward commands and gains can be interpreted. Extensive simulations demonstrate the robustness of the approach to changing environments, outperforming a model-free gradient policy based methods on the same tasks in simulation. Finally, we show that the learned policy can be robustly transferred on a real robot.Comment: IEEE Robotics and Automation Letters 201

Gain-scheduling through continuation of observer-based realizations-applications to H∞ and μ controllers

The dynamic behavior of gain scheduled controllers is highly depending on the state-space representations adopted for the family of lienar controllers designed on a set of operating conditions. In this paper, a technique for determining a set of consistent and physically motivated linear state-space transformations to be applied to the original set of linear controllers is proposed. After transformation, these controllers exhibits an-observer-based structure are therefore easily interpolted and implemented

A model-free control strategy for an experimental greenhouse with an application to fault accommodation

Writing down mathematical models of agricultural greenhouses and regulating them via advanced controllers are challenging tasks since strong perturbations, like meteorological variations, have to be taken into account. This is why we are developing here a new model-free control approach and the corresponding intelligent controllers, where the need of a good model disappears. This setting, which has been introduced quite recently and is easy to implement, is already successful in many engineering domains. Tests on a concrete greenhouse and comparisons with Boolean controllers are reported. They not only demonstrate an excellent climate control, where the reference may be modified in a straightforward way, but also an efficient fault accommodation with respect to the actuators

Soft computing applications in dynamic model identification of polymer extrusion process

This paper proposes the application of soft computing to deal with the constraints in conventional modelling techniques of the dynamic extrusion process. The proposed technique increases the efficiency in utilising the available information during the model identification. The resultant model can be classified as a ‘grey-box model’ or has been termed as a ‘semi-physical model’ in the context. The extrusion process contains a number of parameters that are sensitive to the operating environment. Fuzzy ruled-based system is introduced into the analytical model of the extrusion by means of sub-models to approximate those operational-sensitive parameters. In drawing the optimal structure for the sub-models, a hybrid algorithm of genetic algorithm with fuzzy system (GA-Fuzzy) has been implemented. The sub-models obtained show advantages such as linguistic interpretability, simpler rule-base and less membership functions. The developed model is adaptive with its learning ability through the steepest decent error back-propagation algorithm. This ability might help to minimise the deviation of the model prediction when the operational-sensitive parameters adapt to the changing operating environment in the real situation. The model is first evaluated through simulations on the consistency of model prediction to the theoretical analysis. Then, the effectiveness of adaptive sub-models in approximating the operational-sensitive parameters during the operation is further investigated