Feedback Control Theory in Stochastic Dynamical Systems

This chapter introduces and treats the topic of quantum feedback control on linear quantum systems. Two distinct approaches to feedback control of quantum systems are considered: measurement-based feedback control and coherent feedback control. For measurement-based feedback control, the notions of controlled Hudson–Parthasarathy QSDEs and controlled quantum filtering equations are introduced. Three control problems are formulated and solved: measurement-based linear quadratic Gaussian control, coherent linear quadratic Gaussian control, and coherent feedback \(H^{\infty }\) control. Examples are provided to illustrate each control method.

Behavior can be regarded as the output of a system (action), as a function linking stimulus to response (reaction), or as an abstraction of the bidirectional relationship between the environment and the organism (interaction). When considering the latter possibility, a relevant question arises concerning how an organism can materially and continuously implement such a relationship during its lifetime in order to perpetuate itself. The feedback control approach has taken up the task of answering just that question. During the last several decades, said approach has been progressing and has started to be recognized as a paradigm shift, superseding certain canonical notions in mainstream behavior analysis, cognitive psychology, and even neuroscience. In this paper, we describe the main features of feedback control theory and its associated techniques, concentrating on its critiques of behavior analysis, as well as the commonalities they share. While some of feedback control theory's major critiques of behavior analysis arise from the fact that they focus on different levels of organization, we believe that some are legitimate and meaningful. Moreover, feedback control theory seems to blend with neurobiology more smoothly as compared to canonical behavior analysis, which only subsists in a scattered handful of fields. If this paradigm shift truly takes place, behavior analysts-whether they accept or reject this new currency-should be mindful of the basics of the feedback control approach.

In this research, a security architecture based on the feedback control theory has been proposed. The first loop has been designed, developed and tested. The architecture proposes a feedback model with many controllers located at different stages of network. The controller at each stage gives feedback to the one at higher level and a decision about network security is taken. The first loop implemented in this thesis detects one important anomaly of virus attack, rate of outgoing connection. Though there are other anomalies of a virus attack, rate of outgoing connection is an important one to contain the spread. Based on the feedback model, this symptom is fed back and a state model using queuing theory is developed to delay the connections and slow down the rate of outgoing connections. Upon implementation of this model, whenever an infected machine tries to make connections at a speed not considered safe, the controller kicks in and sends those connections to a delay queue. Because of delaying connections, rate of outgoing connections decrease. Also because of delaying, many connections timeout and get dropped, reducing the spread. PID controller is implemented to decide the number of connections going to safe or suspected queue. Multiple controllers can be implemented to control the parameters like delay and timeout. Control theory analysis is performed on the system to test for stability, controllability, observability. Sensitivity analysis is done to find out the sensitivity of the controller to the delay parameter. The first loop implemented gives feedback to the architecture proposed about symptoms of an attack at the node level. A controller needs to be developed to receive information from different controllers and decision about quarantining needs to be made. This research gives the basic information needed for the controller about what is going on at individual nodes of the network. This information can also be used to increase sensitivity of other loops to increase the effectiveness of feedback architecture.

In this paper, a systematic design procedure for generalized projective synchronization between two identical chaotic satellites systems based on feedback control theory is proposed. This method is developed based on suitable feedback control, combined with the Lyapunov stability theory and linear matrix inequality formulation as a solution of the optimal problem. Two necessary and sufficient conditions for the asymptotic stability of the error dynamic system are obtained. Compared with the predictive-based control method, the proposed method shows comparable and superior performance. The effectiveness of the obtained results is illustrated by numerical simulations.

It is well known that real op-amps do not share most of the desirable characteristics of an ideal one, particularly those of gain and output impedance. When presented with a capacitive load, such as a MOSFET or ADC, feedback in an op-amp circuit can quickly become unstable. This thesis studies and characterizes an op-amp’s output impedance and how its interaction with this type of load creates a parasitic pole which leads to instability. Applying ideas from feedback control theory, a model for studying the problem is developed from which a generalized method for compensating the undesirable circumstance is formulated. Even in a zero-input state, many real op-amps driving capacitive loads can experience unforced oscillations. A case study is performed with three commonly used devices. First, the output impedance is determined by its dependence on the unity-gain bandwidth, load capacitance, and oscillation frequency. It is fitted into a second-order feedback control model that allows for an analytical study of the problem. It is then shown that a carefully designed passive network can be introduced between the load and op-amp to obtain a properly damped system free of oscillation and well-behaved. Using a shunt resistor is a known and commonly used method for lowering an op-amp’s output impedance to gain stability. This work considers the converse addition of a series capacitor to instead lower the load capacitance seen by the op-amp, a seemingly complementary method that achieves the same goal. A generalized, composite compensation method is developed that uses both the shunt resistor and series capacitor– a strategy not yet found in literature. Relevant formulas for damping ratio and natural frequency are derived that allow the design of a passive compensation network. Furthermore, tradeoffs between compensation, voltage swing, current consumption, and power usage are considered. An emphasis is placed on comparing simulated versus real circuits to highlight the fact that any problem is much worse in real-life than in a simulation. SPICE models and programs aim to de-idealize certain device characteristics, but often cannot account for environmental conditions and manufacturing variance. Thus, an importance is placed on experimental verification guided by simulations.

As a specific trait of quantum mechanics, quantum superposition is exploited in many applications such as quantum computation. This paper proposes a feedback scheme to stabilize the desired quantum superposition states. To this aim, a new factorization is derived for the stochastic master equation of a quantum system which is driven by the field in the superposition of coherent states. Then, a feedback scheme is proposed, which consists of a quantum system driven by the field in the superposition of coherent states and a classical feedback channel proportional to the observations of a Homodyne detector. Afterward, the quantum filter of the closed loop system is attained using the SLH framework. Finally, the factorization of the closed loop quantum filter is obtained and the control law is calculated such that the proposed factorization satisfies the stabilization condition. Finally, as an example, the control method is simulated for a two-level atom and the stabilization of the superposition states is achieved.

The purpose of this paper is to describe some recent results concerning optimal feedback control of quantum systems using risk-sensitive performance criteria. We employ quantum stochastic models to describe an important class of quantum systems and define a risk-sensitive criterion for these models. A suitable information state is introduced to solve the optimal control problem using dynamic programming. The results are illustrated by examples

Complex principal oscillation pattern (CPOP) analysis is introduced as an extension of conventional POP analysis. Both are intended to resolve regular evolving patterns from processes with many degrees of freedom. While POP analysis, like many other techniques, deals with the concept of the system state as a real vector, it is argued that this notion be extended into the complex domain. The approach used here results from a critical review of the theory of linear systems of first order. It turns out that these systems cannot appropriately model standing oscillations. The notion of the traveling rate of a mode is defined, and it is demonstrated that the mode's frequency and traveling rate are directly coupled via the system matrix. One consequence is that clean standing oscillations cannot be modeled by linear systems of first order. CPOP analysis introduces a new vector of state. By defining the complex state “state + i · momentum,” both the conventional state itself and its momentum are simultaneously described. The method is capable of resolving oscillatory patterns of any given traveling rate from a stationary process. First experiments show that the CP0Ps evolve more regularly and with less noise than corresponding P0Ps. A prediction scheme that is appropriate for CP0Ps is defined by introducing a transformation technique that can be considered as a causal Hilbert transform. With this scheme prediction skills that are significantly stronger than those of the POP model are gained.

In this paper, we utilize a feedback strategy to stabilize a single qubit in a non-Markovian environment with a Lorentzian spectrum. The non-Markovian single qubit is represented in an augmented system model, where an ancillary system is introduced as the internal mode of the environment to generate Lorentzian noise. The density matrix of the single qubit can be estimated by using an augmented-system-based quantum stochastic master equation. Then a feedback controller can be driven by the estimates to stabilize the qubit in a target state. Simulations show the feedback strategy can provide effective control of the non-Markovian single qubit.

On stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls

Quantum feedback control is a technology that can be used to drive a quantum system into a predetermined eigenstate. In this article, sufficient conditions for the experiment parameters of a quantum feedback control process of a homodyne measurement are given to guarantee feedback control of a spin-$1∕2$ quantum system in case of imperfect detection efficiency. For the case of pure states and perfect detection efficiency, time scales of feedback control processes are calculated.

Dynamical systems with many degrees of freedom can evolve (or be driven) into a stationary state exhibiting scale invariant spatial and/or temporal fluctuations. General arguments are supported by numerical simulations of simple models. Scaling exponents are defined and calculated. We suggest that the concept presented here has wide potential applications, including fractal patterns, 1/f noise, randomly pinned surfaces or interfaces, glasses, and earthquakes. Some of the applications are discussed in detail.

Modeling and simulation of feedwater control system with multiple once-through steam generators in a sodium-cooled fast reactor (II): Control system simulation

Vibration control of tall buildings

The 3~5um Medium Wave Infrared(MWIR) laser has gained a lot of attention for its important application values in remote sensing, medical, military and many other fields. However, there are many technical difficulties to fabricate those kind lasers, and the performance of their output power stabilities remain to be improved. In a practical application, the MWIR’s output power will be instability when the temperature changes and the current varies. So a system of reducing MWIR power fluctuation should be established. In this paper, a photoelectric system of stabilizing the output power of He-Ne laser is developed, which is designed based on the theory of feedback control. Some primary devices and technologies are presented and the functions of each module are described in detail. Among of those, an auxiliary visible light path is designed to aid to adjust WMIR optical system. A converging lens as spatial filter is employed to eliminate stray light well. Dewar temperature control equipment is also used to reduce circuit noise in IR detector. The power supply of AD conversion circuit is independently designed to avoid the crosstalk caused by the analog section and digital section. Then the system has the advantages of good controllability, stability and high precision after above designation. Finally, the measurement precision of the system is also analyzed and verified.