On Rényi information for ergodic diffusion processes

In this paper, we derive explicit formulas of the Rényi information, Shannon entropy and Song measure for the invariant density of one dimensional ergodic diffusion processes. In particular, the diffusion models considered include the hyperbolic, the generalized inverse Gaussian, the Pearson, the exponential family and a new class of skew-t diffusions.     

Optimal nominal dual control for discrete-time linear-quadratic Gaussian problems with unknown parameters

The dual control for a class of discrete-time linear-quadratic Gaussian problems with unknown parameters is studied in this paper. To achieve an optimality in dual control, a control law must possess a property of active learning. The best possible (partial) closed-loop feedback control law is derived in this paper by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing an optimal nominal control law.     

Ergodic control problem for one-dimensional diffusions with near-monotone cost

The existence and uniqueness of the solution to the Bellman equation for ergodic control of one-dimensional diffusions is established under a ‘near-monotonicity’ condition on the cost. Necessary and sufficient conditions for the optimality of a stable Markov control are given in terms of the same.     

Joint segmentation of multivariate Gaussian processes using mixed linear models

The joint segmentation of multiple series is considered. A mixed linear model is used to account for both covariates and correlations between signals. An estimation algorithm based on EM which involves a new dynamic programming strategy for the segmentation step is proposed. The computational efficiency of this procedure is shown and its performance is assessed through simulation experiments. Applications are presented in the field of climatic data analysis.     

Singular control of stochastic linear systems with recursive utility

We formulate a class of singular stochastic control problem with recursive utility where the cost function is determined by a backward stochastic differential equation. Some characteristics of the value function of the control problem are obtained by the method of approximation via penalization, and the optimal control process is constructed.     

Optimality conditions for impulsive control of piecewise-deterministic processes

In this paper we formulate new general optimality conditions for impulsive control of piecewise-deterministic processes. We prove continuity of the value functions for optimal stopping, discounted impulsive control, and impulsive control with long run average cost. We study conditions for optimal and nearly optimal policies for the corresponding impulsive control problems. We give variational formulations of the optimality conditions.This work was done during the author's stay at University of Bonn under grant DAAD 314/104/007/0.     

Iterative learning model predictive control for multi-phase batch processes

Multi-phase batch process is common in industry, such as injection molding process, fermentation and sequencing batch reactor; however, it is still an open problem to control and analyze this kind of processes. Motivated by injection molding processes, the multi-phase batch process in each cycle is formulated as a switched system with internally forced switching instant. Controlling multi-phase batch processes can be decomposed into two subtasks: detecting the dynamics-switching-time; designing the control law for each phase with considering switching effect. In this paper, it is assumed that the dynamics-switching-time can be obtained in real-time and only the second subtask is studied. To exploit the repetitive nature of batch processes, iterative learning control scheme is used in batch direction. To deal with constraints, updating law is designed by using model predictive control scheme. An online iterative learning model predictive control (ILMPC) law is first proposed with a quadratic programming problem to be solved online. To reduce computation burden, an offline ILMPC is also proposed and compared. Applications on injection molding processes show that the proposed algorithms can control multi-phase batch processes well.     

Singular optimal control problems: On the order of a singular arc

The higher-order tests for optimality of singular arcs in optimal control problems, as well as the characterization of the continuity and smoothness properties of the optimal control at points, called junctions, joining nonsingular and singular arcs of the control, depend upon the orders of the arcs involved. To data, definitions of order have been rigorously given only for terminal unconstrained control problems or by means of a normality assumption in the order cases. We give here a new definition of the local order of a singular arc which unifies those already given in the literature. One advantage of the proposed definition is that, unlike the previous ones, it remains valid even when there are terminal constraints. One example will illustrate the fact that such a basic concept is essential to solve the very difficult synthesis problem as soon as the dimension of the state space is greater than two.     

Ergodic control of partially observed Markov chains

The ergodic or long-run average cost control problem for a partially observed finite-state Markov chain is studied via the associated fully observed separated control problem for the nonlinear filter. Dynamic programming equations for the latter are derived, leading to existence and characterization of optimal stationary policies.     

Near optimality conditions in stochastic control of jump diffusion processes

This paper is concerned with necessary as well as sufficient conditions for near-optimality of controlled jump diffusion processes. Necessary conditions for a control to be near-optimal are derived, using Ekeland’s variational principle and some stability results on the state and adjoint processes, with respect to the control variable. In a second step, we show that the necessary conditions for near-optimality, are in fact sufficient for near-optimality provided some concavity conditions are fulfilled. Finally, as an illustration some examples are solved explicitly.     

Asymptotics in quasi-variational inequalities and ergodic control problems

For some class of discounted impulse-control problems and the corresponding inequalities satisfied by the optimal cost, we study the asymptotic behaviour when the discount factor goes to zero. We use the semi-group formulation of the QVI.Using the previous results on that subject, we obtain estimates of the convergence.     

Ergodic impulsive control of Feller processes with costly information

In this paper we study the problem of ergodic impulsive control of Feller processes with costly information. We prove continuity of the value functions for optimal stopping and impulsive control with long run average cost. We characterize the value functions as generalized solutions of respective quasi-variational inequalities and describe optimal policies. We study also an equation associated to impulsive control with long run average cost.     

PID based nonlinear processes control model uncertainty improvement by using Gaussian process model

Proportional-integral-derivative (PID) controller design based on the Gaussian process (GP) model is proposed in this study. The GP model, defined by its mean and covariance function, provides predictive variance in addition to the predicted mean. GP model highlights areas where prediction quality is poor, due to the lack of data, by indicating the higher variance around the predicted mean. The variance information is taken into account in the PID controller design and is used for the selection of data to improve the model at the successive stage. This results in a trade-off between safety and the performance due to the controller avoiding the region with large variance at the cost of not tracking the set point to ensure process safety. The proposed direct method evaluates the PID controller design by the gradient calculation. In order to reduce computation the characteristic of the instantaneous linearized GP model is extracted for a linearized framework of PID controller design. Two case studies on continuous and batch processes were carried out to illustrate the applicability of the proposed method.     

Optimal control for integrated emission management in diesel engines

Integrated Emission Management (IEM) is a supervisory control strategy that minimises operational costs (consisting of fuel and AdBlue) for diesel engines with an aftertreatment system, while satisfying emission constraints imposed by legislation. In most work on IEM, a suboptimal heuristic real-time implementable solution is used, which is based on Pontryagin's Minimum Principle (PMP). In this paper, we compute the optimal solution using both PMP and Dynamic Programming (DP). As the emission legislation imposes a terminal state constraint, standard DP algorithms are sensitive to numerical errors that appear close to the boundary of the feasible sets. Therefore, we propose two extensions to existing DP methods, which use an approximation of the forward reachable sets to reduce the grid size over time and an approximation of the backward reachable sets to avoid the aforementioned numerical errors. Using a simulation study of a cold-start World Harmonised Transient Cycle for a Euro-VI engine, we show that the novel extension to the DP algorithm yields the best approximation of the optimal cost, when compared to existing DP methods. Furthermore, we show that PMP yields almost the same results as DP, and that the real-time implementable solution only deviates approximately 0.08–0.16% from the optimal solution.     

Optimization method for solving bang-bang and singular control problems

In this paper we study optimal control problems with the control variable appearing linearly.A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented.This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem.The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc.A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming(NLP) problem.The control profiles and stage lengths act as decision variables.Based on the Pontryagin maximal principle,a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers.Two examples are studied to demonstrate the effectiveness of this strategy.     

Robust control strategies for multi-inventory systems with average flow constraints

In this paper, we consider multi-inventory systems in the presence of uncertain demand. We assume that (i) demand is unknown but bounded in an assigned compact set and (ii) the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we select a nominal flow that feeds such a demand. In this context, we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average. We provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows. Such conditions are based on linear programming and thus they are constructive. In the special case of a static flow (i.e. a system with 0-capacity buffers) we show that the strategy must be affine. The dynamic problem can be solved by a linear-saturated control strategy (inspired by the previous one). We provide numerical analysis and illustrative examples.     

Cross-directional control of sheet and film processes

Sheet and film processes include polymer film extrusion, coating processes of many types, paper manufacturing, sheet metal rolling, and plate glass manufacture. Identification, estimation, monitoring, and control of sheet and film processes are of substantial industrial interest since effective control means reduced usage of raw materials, increased production rates, improved product quality, elimination of product rejects, and reduced energy consumption. This paper reviews recent developments in sheet and film process control with particular attention to the effectiveness of existing techniques at addressing the critical aspects of sheet and film processes.     

The application of fuzzy control systems to industrial processes

The paper describes the application of fuzzy algorithms to the control of dynamic processes. The fuzzy control algorithm is used to implement linguistically expressed heuristic control policies directly, with a view to automating those complex and poorly-defined processes where modelling difficulties and lack of suitable measurements make manual control imperative. The results obtained from two pilot-scale studies are presented and the stability of the fuzzy control system is discussed.     

Event-triggered control for mitigating SIS spreading processes

In this paper, we investigate the problem of designing event-triggered controllers for containing epidemic processes in complex networks. We focus on a deterministic susceptible–infected–susceptible (SIS) model, which is one of the well-known, fundamental models that capture the epidemic spreading. The event-triggered control is particularly formulated in the context of viral spreading, in which control inputs (e.g., the amount of medical treatments, a level of traffic regulations) for each subpopulation are updated only when the fraction of the infected people in the subpopulation exceeds a prescribed threshold. We analyze the stability of the proposed event-triggered controller and derive a sufficient condition for a prescribed control objective to be achieved. Moreover, we propose a novel emulation-based approach towards the design of the event-triggered controller, and show that the problem of designing the event-triggered controller can be solved in polynomial time using a geometric programming. We illustrate the effectiveness of the proposed approach through numerical simulations using an air transportation network.