Kwang-Ki K. Kim

Generalised polynomial chaos expansion approaches to approximate stochastic model predictive control

This paper considers the model predictive control of dynamic systems subject to stochastic uncertainties due to parametric uncertainties and exogenous disturbance. The effects of uncertainties are quantified using generalised polynomial chaos expansions with an additive Gaussian random process as the exogenous disturbance. With Gaussian approximation of the resulting solution trajectory of a stochastic differential equation using generalised polynomial chaos expansion, convex finite-horizon model predictive control problems are solved that are amenable to online computation of a stochastically robust control policy over the time horizon. Using generalised polynomial chaos expansions combined with convex relaxation methods, the probabilistic constraints are replaced by convex deterministic constraints that approximate the probabilistic violations. This approach to chance-constrained model predictive control provides an explicit way to handle a stochastic system model in the presence of both model uncertainty and exogenous disturbances.

Filter Design for ℒ 1 Adaptive Output-Feedback Controller

In this paper we exploit the connection between disturbance observer and ℒ<inf>1</inf> adaptive control theories. We consider ℒ<inf>1</inf> adaptive output-feedback control framework, for which the ℒ<inf>1</inf> reference controller is equivalent to the disturbance observer. Using this fact, we investigate several properties of the disturbance observer architecture, leading to various filter design methods towards verification of the stability conditions for the ℒ<inf>1</inf> adaptive output-feedback controller.

Generalized polynomial chaos expansion approaches to approximate stochastic receding horizon control with applications to probabilistic collision checking and avoidance

This paper studies the model predictive control of dynamic systems subject to stochastic parametric uncertainty due to plant/model mismatches and exogenous disturbance that corresponds to uncertain circumstance in operation of the system. Model and disturbance uncertainties are ubiquitous in any mathematical models of system and control theory. Parametric uncertainty propagation or quantification is approximated using a spectral method called polynomial chaos expansion and exogenous disturbance is assumed to be an additive Gaussian random process. With Gaussian approximation of resulting solution trajectory of a stochastic differential equation using polynomial chaos expansion, we solve convex finite-horizon model predictive control problems that are amenable to online computation of a stochastically robust control policy over the time-horizon. The proposed approach to chance-constrained model predictive control provides an explicit way to handle a stochastic system model in the presence of both model uncertainty and exogenous disturbances. Probabilistic constraints are replaced by convex deterministic constraints that approximate the probabilistic violations with a user-defined confidence level.

Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-Offs

Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional time-varying Gauss-Markov processes under mean-square distortion criteria. We first revisit the sensor-estimator separation principle, which asserts that considered SRD problem is equivalent to a joint sensor and estimator design problem in which data-rate of the sensor output is minimized while the estimators performance satisfies the distortion criteria. We then show that the optimal joint design can be performed by semidefinite programming. A semidefinite representation of the corresponding SRD function is obtained. Implications of the obtained result in the context of zero-delay source coding theory and applications to networked control theory are also discussed.

Probabilistic analysis and control of uncertain dynamic systems: Generalized polynomial chaos expansion approaches

Uncertainties are ubiquitous in mathematical models of complex systems and this paper considers the incorporation of generalized polynomial chaos expansions for uncertainty propagation and quantification into robust control design. Generalized polynomial chaos expansions are more computationally efficient than Monte Carlo simulation for quantifying the influence of stochastic parametric uncertainties on the states and outputs. Approximate surrogate models based on generalized polynomial chaos expansions are applied to design optimal controllers by solving stochastic optimizations in which the control laws are suitably parameterized, and the cost functions and probabilistic (chance) constraints are approximated by spectral representations. The approximation error is shown to converge to zero as the number of terms in the generalized polynomial chaos expansions increases. Several proposed approximate stochastic optimization problem formulations are demonstrated for a probabilistic robust optimal IMC control problem.

Universal approximation with error bounds for dynamic artificial neural network models: A tutorial and some new results

The three main classes of dynamic artificial neural network models for identification of nonlinear dynamical systems are reviewed: (1) neural state-space models, (2) global input-output models, (3) dynamic recurrent neural network models. The presentation of the mathematical models and architectures are followed by their representations in terms of a consistent block diagram convenient for stability and performance analyses and argued to potentially have benefits for process identification. The classes of nonlinear dynamical systems that are universally approximated by such models are characterized, with rigorous upper bounds on the approximation errors. While many of the results are available in the literature, this paper is the first to fully develop and clearly explain these models and their interrelationships to provide a broader perspective, and presents some new results to fill in the gaps in the literature.

Clinico-electrical Characteristics of Lateral Temporal Lobe Epilepsy; Anterior and Posterior Lateral Temporal Lobe Epilepsy

Background and Purpose This study aimed to determine whether there are clinicoelectrical differences between anterior lateral temporal lobe epilepsy (ALTLE) and posterior lateral temporal lobe epilepsy (PLTLE), taking medial temporal lobe epilepsy (MTLE) as a reference. Methods We analyzed the historical information, ictal semiologies, and ictal EEGs of temporal lobe epilepsy patients with a documented favorable surgical outcome (Engel class I or II) at follow-up after more than one year. LTLE was defined when a discrete lesion on MRI or an ictal onset zone in invasive study was located outside the collateral sulcus. LTLE was further divided into ALTLE and PLTLE by reference to the line across the cerebral peduncle. Total 107 seizures of 13 ALTLE, 8 PLTLE and 21 MTLE patients were reviewed. Results Initial hypomotor symptom was frequently observed in PLTLE (P<0.001). Oroalimentary automatism (OAA) was not observed initially in PLTLE. Generalized tonic-clonic seizures occurred significantly earlier in PLTLE than in ALTLE or MTLE (P< 0.001). Ictal scalp EEG was not helpful in differentiating between ALTLE and PLTLE. Conclusions Frequent hypomotor onset, the absence of initial oroalimentary automatism, and early generalization are characteristic findings of PLTLE, although they are insufficient to differentiate it from ALTLE or MTLE.

Robustness Analysis, Prediction and Estimation for Uncertain Biochemical Networks

Abstract Mathematical models of biochemical reaction networks are important tools in systems biology and systems medicine to understand the reasons for diseases like cancer, and to make predictions for the development of effective treatments. In synthetic biology, for instance, models are used for the design of circuits to reliably perform specialized tasks. For analysis and predictions, plausible and reliable models are required, i.e., models must reflect the properties of interest of the considered biochemical networks. One remarkable property of biochemical networks is robust functioning over a wide range of perturbations and environmental conditions. Plausible mathematical models of such robust networks should also be robust. However, capturing, describing, and analyzing robustness in biochemical reaction networks is challenging. First, including uncertainty in the structures, parameters, and perturbations into the model is not straightforward due to different types of uncertainties encountered. Second, robustness as well as system and thus model properties are often itself inherently uncertain, such as qualitative (i.e., nonquantitative) descriptions. Finally, analyzing nonlinear models subject to different uncertainties and with respect to quantitative and qualitative properties is still in its infancy. In the first part of this perspective article, network functions and behaviors of interest are formally defined. Furthermore, different classes of uncertainties and perturbations in the data and model are consistently described. In the second part, we review frequently used approaches and present our own recent developments for robustness analysis, estimation, and model-based prediction. We illustrate their capabilities to deal with the different types of uncertainties and robustness requirements.

Multi-Criteria Optimization for Filter Design of L1 Adaptive Control

This paper considers the problem of optimal trade-off between robustness, in terms of time-delay margin, and performance of the

Fast moving horizon estimation for a two-dimensional distributed parameter system

\mathcal {L}_{1}