Abstracts:The problem of boundary stabilization of thermoacoustic oscillations in the Rijke tube is investigated using the backstepping method; as a first step, this work only considers the full-state design. This system consists of a vertical tube open at both ends and a heater placed in the lower half of the tube. To study this problem we consider that the mathematical model takes the form of 2 $\times$ 2 linear first-order hyperbolic partial differential equations (PDEs) with a point source term (induced by the Dirac delta distribution) on the right hand side, plus the coupling of an ordinary differential equation (ODE), and control input at one boundary condition. The presence of the Dirac delta distribution implies that the system solution has a discontinuity on a point of the domain, but is continuous everywhere else. We use a coordinate transformation to rewrite the equations into a system of four transport PDEs convecting in opposite directions and to translate the discontinuity to the boundary conditions. Then, a full state feedback backstepping controller is designed to exponentially stabilize the origin. However, the model is non-strict-feedback making unfeasible the use of standard backstepping designs. This issue is tackled by formulating a well-posed and invertible integral transformation with Volterra and Fredholm terms that maps the Rijke system into a target system with desirable stability properties. An exact piecewise-differentiable expression for the kernels of this transformation is found, allowing us in turn to derive an explicit feedback control law. Simulation results are presented to illustrate the effectiveness of the proposed control design.

Abstracts:The purpose of this paper is to present a network realization theory for a class of mixed quantum–classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum–classical systems are proposed. Necessary and sufficient conditions for their physical realizability are derived. Based on these physical realizability conditions, a network synthesis theory for this class of linear mixed quantum–classical systems is developed, which clearly exhibits the quantum component, the classical component, and their interface. An example is used to illustrate the theory presented in this paper.

Abstracts:This paper defines a generalized probabilistic linear latent variable model (GPLLVM) that under specific restrictions reduces to various probabilistic linear models used for process monitoring. For the defined model, we rigorously derive the monitoring statistics and their respective null distributions. Monitoring statistics of the defined model also reduce to the monitoring statistics of various probabilistic models when restricted with the corresponding conditions. The paper presents insightful equivalence between the classical multivariate techniques for process monitoring and their probabilistic counterparts, which is obtained by restricting the generalized model. We also provide an estimation approach based on the expectation maximization algorithm (EM) for GPLLVM. The results presented in the paper are verified using numerical simulation examples.

Abstracts:In this paper, we propose the periodic event-triggering based design of sliding mode control (SMC) for the linear time-invariant (LTI) systems. In this technique, the triggering instants are generated by a triggering mechanism which is evaluated periodically at those time instants when the state measurements are available. So, the continuous state measurement, as it is usually needed in the continuous event-triggering strategy, is no longer required in this proposed triggering strategy. The main advantages of this triggering mechanism are: (1) a uniform positive lower bound for the inter event time is guaranteed and (2) this technique is more economical and realistic than its continuous counterpart due to the relaxation of continuous measurements. In this work, we use SMC to design the periodic event-triggering condition where SMC is designed in such a way that it allows periodic evaluation of triggering rule while guaranteeing the robust performance of the system. Moreover, an upper bound of the sampling period for the periodic measurements is also obtained in this design. Finally, the simulation results are given to demonstrate the design methodology and performance of the system with the proposed event-triggering strategy.

Abstracts:Using semi-tensor product of matrices, the vector space structure of Boolean games and their some specified subsets are proposed. By resorting to the vector space structure and potential equation, we give an alternative proof for the fact that a symmetric Boolean game is a potential game. The two advantages of this new approach are revealed as follows: (1) It can provide the corresponding potential function; (2) It can be used to explore new potential Boolean games. The corresponding formula is provided to demonstrate the first advantage. As for the second one, the renaming symmetric Boolean games and the weighted symmetric Boolean games are also proved to be potential and weighted potential respectively. Moreover, as a non-symmetric game, the flipped symmetry Boolean game has been constructed and proved to be potential.

Abstracts:Most stochastic Model Predictive Control (MPC) formulations allow constraint violations via the use of chance constraints, thus increasing control authority and improving performance when compared to their robust MPC counterparts. However, common stochastic MPC methods handle chance constraints conservatively: constraint violations are often smaller than allowed by design, thus limiting the potential improvements in control performance. This is a consequence of enforcing chance constraints overlooking the past behavior of the system and/or of an over tightening of the constraints on the predicted sequences. This work presents a stochastic MPC strategy that uses the observed amount of constraint violations to adaptively scale the tightening parameters, thus eliminating the aforementioned conservativeness. It is proven using Stochastic Approximation that, under suitable conditions, the amount of constraint violations converges in probability when using the proposed method. The effectiveness and benefits of the approach are illustrated by a simulation example.

Abstracts:In this paper, we consider a class of general linear forward and , backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ optimal control problem are then studied as applications. First, we derive the optimal solution to the classic stochastic LQ problem by applying the solution to the associated FBSDEs. Secondly, we study a new type of LQ problem governed by a forward–backward stochastic system (FBSS). By applying the maximum principle and the solution to FBSDEs, an explicit solution is given in terms of a Riccati equation. Finally, by exploring the asymptotic behavior of the Riccati equation, we derive an equivalent condition for the mean-square stabilizability of FBSS.

Abstracts:In this paper, we consider boundary output tracking for a one-dimensional heat equation with external disturbance at the opposite end of the bar. First, an unknown input infinite-dimensional observer is designed and an estimate of disturbance is obtained from the observer. Second, with reference signal and estimate of disturbance, we design a servo system which has bounded solution given that the reference signal and its derivative are bounded. The output feedback boundary control is then designed by the states of servo system and observer. It is proved that the state of closed-loop system tracks the state of the servo system. As a result, the output tracking is included. Finally, some simulation results are presented to illustrate the effectiveness of the proposed scheme.

Abstracts:In this work, we consider the optimal sensory data scheduling of multiple process. A remote estimator is deployed to monitor $S$ independent linear time-invariant processes. Each process is measured by a sensor, which is capable of computing a local estimate and sending its local state estimate wrapped up in packets to the remote estimator. The lengths of the packets are different due to different dynamics of each process. Consequently, it takes different time durations for the sensors to send the local estimates. In addition, only a portion of all the sensors are allowed to transmit at each time due to bandwidth limitation. We are interested in minimizing the sum of the average estimation error covariance of each process at the remote estimator under such packet transmission and bandwidth constraints. We formulate the problem as an average cost Markov decision process (MDP) over an infinite horizon. We first study the special case when $S=1$ and find that the optimal scheduling policy always aims to complete transmitting the current estimate. We also derive a sufficient condition for boundedness of the average remote estimation error. We then study the case for general $S$. We establish the existence of a deterministic and stationary policy for the optimal scheduling problem. We find that the optimal policy has a consistent property among the sensors and a switching type structure. A stochastic algorithm is designed to utilize the structure of the policy to reduce computation complexity. Numerical examples are provided to illustrate the theoretical results.

Abstracts:We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determines the shape of the resulting jump model.