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The standard extensive-form partitional representation of information in sequential games fails to distinguish the description of the rules of interaction from the description of players' personal traits. Indeed, this representation does not model how the information given to players as per the rules of the game blends with players' cognitive abilities. We propose a representation of sequential games that explicitly describes the flow of information accruing to players rather than the stock of information retained by players encoded in information partitions. Then, we add a game-independent description of players' mnemonic abilities. If players have perfect memory, our flow representation gives rise to information partitions satisfying the perfect recall property, but different combinations of information flows and players' mnemonic abilities may induce the same information partitions. We show how to use our framework to explicitly model a wide array of cognitive limitations and embed them in the representation of game situations. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach to design interval observer–based compensator for linear systems with uncertain parameters and measurement noises. Based on monotone system theory, existence decoupled conditions of observers gain design to guarantee cooperativity and input-to-state stability of error dynamics system are proposed in terms of a set of linear matrix inequalities. Moreover, a compensator consisting of the observers and output feedback controller is designed within interval observer design framework. Such an observer-based compensator has a simple separation structure, which shows that interval observers and feedback controller can be simultaneously designed based on separation principle. The developed techniques on observer-based compensator design are illustrated through a practical example. [ABSTRACT FROM AUTHOR]

This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.

A permit sharing problem is described by a list of countries, each of which owns a certain amount of emission permits and has a unique technology that requires permits to produce output. We consider the solutions of sharing the optimal global surplus generated beyond the autarky economy output. We divide countries into two groups based on the types of contribution, the technology contributors and the permit contributors. Suppose that the division of the total surplus between the two groups is fixed at an arbitrary ratio α ∈ [ 0 , 1 ] (Separation Principle of parameter α ). The fixed amount of surplus assigned to each group is distributed based on the contributions of the members of the group. By requiring that no subgroup of countries can increase their share by reallocating the total amount of their contributions among themselves (Permit Reallocation-Proofness and Technology Reallocation-Proofness), we characterize a family of solutions indexed by parameter α ∈ [ 0 , 1 ] , called the proportional solution of parameter α . By further requiring that each country receives at least the level of output it can produce with its own technology and permit (Voluntary Participation), we show that only the solution with α = 1 / 2 , called the equal share proportional solution, meets this requirement. Under this solution, the technology contributors and the permit contributors are treated equally. [ABSTRACT FROM AUTHOR]

In linear systems, it is well known that any combination of stabilizing state feedback controller and a state observer results in the output feedback controller which asymptotically stabilizes the closed-loop system. This is known as the separation principle, which does not generally hold for nonlinear systems. For nonlinear systems, the output feedback problem is usually pursued by extending the results of observer synthesis, which itself is a challenging problem. In this paper, we investigate the stabilization via an observer configuration problem for some classes of nonlinear time-varying systems by using new integral inequalities of Gronwall type. Given that the sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimated state feedback from the proposed practical observer will achieve the global practical exponential stabilization. Furthermore, the effectiveness of the proposed scheme is shown through simulation for two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global practical uniform h-stability analysis problem for a certain class of nonlinear non-autonomous systems where the associated nominal system is linear that depends on the time t and the perturbation term satisfies some conditions. Moreover, with the help of the new notion of practical h-stable functions, we study the separation principle in the practical sense for two classes of nonlinear non-autonomous systems having a nominal linear part. We propose some classes of memoryless state linear and nonlinear feedback controllers. Furthermore, an illustrative example is given to demonstrate the applicability of main result. [ABSTRACT FROM AUTHOR]

This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable. [ABSTRACT FROM AUTHOR]

This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances. In case there is no perturbation, the exponential convergence of the observer was confirmed. When external disturbances appear in the system, a separation principle is established, and the authors show that the closed loop system is exponentially practical stable. By choosing a suitable Lyapunov-Krasovskii functional, the authors derive new sufficient conditions to guarantee the exponential stability of the systems. Finally, a physical model is performed to prove the efficiency and applicability of the suggested approach. [ABSTRACT FROM AUTHOR]

Taxes are the most important source of funding for the provision of public services. The best way to ensure tax revenue is to keep tax resistance to a minimum. The best way to keep tax resistance to a minimum is to build a fair tax system. Tax compliance of taxpayers is expected to be increased through a fair tax system. While creating the tax system, taxation is made according to two approaches. It is the benefit or also the utilization approach and the power of payment or the power approach. The most important indicator of solvency is income. Other payment powers are also expressed in income. While the part of income that is reserved for consumption is called spending, the part that is allocated to savings is called wealth. Therefore, indicators of ability to pay; it consists of income, wealth and spending. Various methods are also used in reaching the ability to pay. Progressive taxation, separation principle and minimum livelihood allowance are the methods used to reach the ability to pay. In this study, it will be focused on how the methods used to reach ability to pay are applied in selected EU countries, its effect on tax revenue and its relationship with fair taxation. In the study, rather than discussing whether the systems are fair or not, the relationship between ability to pay and tax justice will be revealed by using data on the methods used to reach ability to pay. In the study, using the data of EU member countries, literature review and data analysis method were applied. Through work; It is aimed to contribute to the literature by revealing the relationship between justice in tax and justice perception by using the methods applied in reaching the ability to pay. As a result of the study, it was found that the tax systems in EU member countries are different, they apply the methods used to reach the ability to pay in different ways, and this creates an obstacle to generalization.

Consider a linear time-varying (LTV) system described by the state-space equation x = A(t)x + B(t)u(t). The main objectives of this paper include (i) determination of the analytical or closed-form solutions for the fundamental matrix X(t) and the state transition matrix (t,to) Φ of the LTV system; (ii) design of feedback control, such that the closed-loop system matrix Acl (t) = A(t)-B(t)K(t), where K(t) is a gain matrix, has desirable properties, in particular, Acl (t) being commutative and triangular; and (iii) design of observers such that the observer matrix Ao(t)=A(t)-H(t)C(t), where H(t) is the observer gain matrix, has desirable properties as in (ii), namely, Ao(t) being commutative and triangular. The commutativity and triangularization of Acl(t) and Ao(t) facilitate the analytical solutions for their fundamental and state transition matrices. Examples and simulations demonstrate the design objectives. [ABSTRACT FROM AUTHOR]

In this paper, a new speed control algorithm for a permanent magnet DC motor which does not require implementation of the angular speed sensor is presented. Three steps are performed to develop the control system: design of speed tracking control algorithm assuming the speed measurement; design of speed observer; design of sensorless speed control algorithm based on the principle of separation. Information about speed is taken from the speed observer using the motor current value. The stability of the composite system dynamics consisting of three subsystems (the speed regulation loop, current regulation loop, and speed observer) is analyzed. The feedback gains tuning procedure for decoupling of three subsystems is given. The simulation results show that the dynamic performance of the designed system is similar to the performance of the system with angular speed measurement. The resulting closed-loop system has structural robustness properties with respect to parametric and coordinate disturbances. References 12, figures 2.

For a controlled linear stochastic differential system, we consider the problem of tracking the jumping state of an additive input action determining the current stabilization direction (drift). The tracking objective, which is to stabilize the system near the varying drift, is formalized by a quadratic performance functional. The input action defines a continuous-time Markov chain. The problem is considered in the cases of complete and incomplete information. Dynamic programming is used to solve it in both cases. The solution of the Bellman equation in the first case is obtained based on the properties of a finite-dimensional chain, and in the second case, based on the principle of separation of control and state estimation problems provided by the Wonham filter estimate and the properties of the quadratic performance criterion. A numerical experiment uses an applied model describing the position of a simple mechanical drive. The results of calculations confirming the applicability of the solutions obtained, as well as ways to overcome the difficulties of their numerical implementation, are presented and discussed in detail. [ABSTRACT FROM AUTHOR]

In this paper, the iterative learning control (ILC) problem is investigated for a class of time-invariant parabolic singular distributed parameter systems. Initially, the singular distributed parameter systems is decomposed into infinite number of singular systems based on the separation principle. Meanwhile, the slow-fast subsystems are introduced via singular value decomposition method. Then, a novel mixed PD-type ILC algorithm with finite dimension is designed for the low dimensional slow part and the corresponding convergence conditions are manifested. With the proposed controller, the output error of high dimensional fast complement can satisfy the given value instead of neglecting the effect of high dimensional modes. Furthermore, under the aforesaid ILC law and the appropriate number of the low dimensional slow part, the resulting tracking error of parabolic singular distributed parameter systems can converge to any small tracking accuracy. Finally, simulation results on the distributed building automatic temperature system verify the convergence and effectiveness of the mixed PD-type ILC algorithm.

Countercurrent chromatography (CCC) is the separation technique based on the different partition coefficients of the sample between two immiscible solvents, which is a liquid-liquid partition without solid support in the column. In this paper, Firstly, the mechanic's equilibrium principle of CCC is described, which includes hydrostatic equilibrium system (HSES), hydrodynamic equilibrium system (HDES), unidirectional hydrodynamic equilibrium phenomenon, etc. The separation principle of the CCC is also explained. Secondly, the mechanical structure and design of parallel-axis CCC, cross-axis CCC, oblique-axis CCC, as well as some CCC derived from the three are illustrated respectively. Finally, the existing problems for the development of CCC have been exposed, and the trend of the future development direction and applications of CCC are discussed. [ABSTRACT FROM AUTHOR]

This article proposes a two-degree-of-freedom fractional-order proportional derivative (FOPD) controller with a general extended state observer (GESO) to achieve both optimal set-speed tracking and disturbance rejection performance for a typical permanent magnet synchronous motor servo system. The GESO simplifies the control plant, estimates and actively rejects total disturbances. The FOPD controller achieves fast speed tracking with almost no overshoot. Furthermore, it is verified that the control system with the proposed FOPD-GESO controller design meets the separation principle through mathematical derivation and simulation illustration. It shows that the proposed controller breaks the inherent tradeoff on tracking performance and disturbance robustness of the typical traditional proportional–integral–derivative (PID) control. Meanwhile, a systematic scheme for designing the FOPD-GESO controller to satisfy both frequency-domain and time-domain specifications is proposed in this article. Simulation illustration and experimental validation are performed to demonstrate that the proposed FOPD-GESO controller is superior to the typical integer-order PID controller, integer-order active disturbance rejection control with a typical extended state observer, and fractional-order PID controller in terms of speed tracking, antiload disturbance, and robustness to internal uncertainties. [ABSTRACT FROM AUTHOR]

This paper focuses on a dynamic multi‐asset mean‐variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and correlation matrix of the assets, and for studying the join effects on portfolio diversification. The dynamic setting allows us to consider time varying ambiguity sets, which include the cases where the drift and correlation are estimated on a rolling window of historical data or when the investor takes into account learning on the ambiguity. In this context, we prove a general separation principle for the associated robust control problem, which allows us to reduce the determination of the optimal dynamic strategy to the parametric computation of the minimal risk premium function. Our results provide a justification for under‐diversification, as documented in empirical studies and in the static models. Furthermore, we explicitly quantify the degree of under‐diversification in terms of correlation bounds and Sharpe ratios proximities, and emphasize the different features induced by drift and correlation ambiguity. In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. We also provide a complete picture of the diversification for the optimal robust portfolio in the three‐asset case. [ABSTRACT FROM AUTHOR]

This paper studies a separation principle for a class of linear sampled-data control systems with aperiodic sampling. The concerned problem is to show that in aperiodic sampling, the design of observer-based output feedback controller can be broken into two separate designs: aperiodic sampled-data static state feedback controller and observer designs. It is proved that asymptotic (respectively, exponential) stabilization by the sampled-data static state feedback and asymptotic (respectively, exponential) observation by the sampled-data Luenberger observer imply asymptotic (respectively, exponential) stabilization by the sampled-data observer-based output feedback. An example is given to check the validity of the proposed theoretical claims.

This article establishes a descriptor regular form and shows its applications in observer‐based integral sliding mode controllers design of descriptor systems. A reduced‐order linear observer and a full‐order descriptor sliding mode observer are, respectively, designed to estimate the state variables of the descriptor system under consideration. Necessary and sufficient conditions for the existence of the proposed descriptor regular form and observers are derived. With the descriptor regular form, it is revealed that the separation principle holds for the proposed observer‐based integral sliding mode control methods. This means that the proposed observers can be designed independently and when using the estimation of state variables obtained from them to replace the state variables in a stabilizing state‐feedback integral sliding mode controller, the resulting observer‐based integral sliding mode controller can still stabilize the descriptor system. Finally, a constrained mechanical system is numerically simulated to verify the methods proposed. [ABSTRACT FROM AUTHOR]

In this paper, we address the state/fault estimation and observer-based control issues for switched systems with sensor faults. The main objective is to estimate sensor faults and compensate for their effects on the system state estimation, and then stabilize the switched system by the estimated state feedback. Applying the mode-dependent average dwell time (MDADT) concept and the Lyapunov stability theory, a new separation principle is developed, which allows formalizing the observer-based controller design in the form of linear matrix inequalities (LMI) instead of bilinear ones. Finally, a highly manoeuvrable aircraft technology (HiMAT) example, a DC–DC boost converter example, and a numerical example are investigated to show the practicability and efficiency of the obtained results. • Simultaneously estimate sensor faults and system states. • Stabilize continuous-time switched systems even in the presence of sensor faults. • Develop a new separation principle to formalize the observer-based controller design in the form of LMIs instead of BMIs. [ABSTRACT FROM AUTHOR]

Over the last 50 years, a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we propose a new framework for establishing the separation principle. This approach takes the viewpoint that stochastic systems are well-defined maps between sample paths rather than stochastic processes per se and allows us to extend the separation principle to systems driven by martingales with possible jumps. While the approach is more in line with 'real-life' engineering thinking where signals travel around the feedback loop, it is unconventional from a probabilistic point of view in that control laws for which the feedback equations are satisfied almost surely, and not deterministically for every sample path, are excluded. © 2013 IEEE.

Summary: In this article, the problem of reduced‐order observer‐based controller design for a class of nonlinear time‐delay systems is addressed. First, we present sufficient conditions for the existence of the reduced‐order observer of nonlinear time‐delay systems. Then, a state feedback controller is designed to stabilize the systems. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the reduced‐order observer‐based controller. When the nonlinear part of systems satisfies the quasi‐one‐sided Lipschitz condition, the reduced‐order observer and feedback controller can be designed separately even though the parameter (A, C) of systems is not detectable and parameter (A, B) is not stabilizable. Finally, a numerical example is presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This study solves the problem of observer‐based output feedback stabilisation of a coupled time‐fractional reaction–advection–diffusion system with space‐dependent coefficients. In light of the backstepping approach, the Mittag–Leffler convergent observer is derived to enable stabilisation by output feedback. By the fractional Lyapunov method, the Mittag–Leffler stability of the estimation error system is then established. Using the separation principle yields a stabilising output feedback controller, with which the closed‐loop stability is proved. Finally, the feasibility of the proposed approach is tested by fractional numerical examples when the kernel matrix equation has not the explicit solution. [ABSTRACT FROM AUTHOR]

In this study, the stabilisation of quasi‐one‐sided Lipschitz non‐linear systems is investigated. For the quasi‐one‐sided Lipschitz non‐linear system, a condition for the existence of the observer is presented. For the weak quasi‐one‐sided Lipschitz non‐linear system, a state feedback controller is proposed and a condition is derived for the existence of the state feedback controller. The separation principle is obtained for the observer‐based controller of the quasi‐one‐sided Lipschitz non‐linear systems. The main results in this study extend and improve those in the literature. Numerical examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Summary: In this article, we address the problem of output stabilization for a class of nonlinear time‐delay systems. First, an observer is designed for estimating the state of nonlinear time‐delay systems by means of quasi‐one‐sided Lipschitz condition, which is less conservative than the one‐sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi‐one‐sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time‐delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results. [ABSTRACT FROM AUTHOR]

Rapid developments in robot technology in the 21st century started to transform society and economy fundamentally. Today, the issue of taxation of smart robots, which is widely used in every field from production to the service sector and leads to increasing economic efficiency as well as technological unemployment, has begun to be addressed with its economic and social dimensions. This study aims to clarify the economic reasons for the necessity of a robot tax by examining the effects of robots on the labor market, income distribution and public financial balance. The findings of this study are as follows; Robot technology will lead to a new global balance in the labor market. In order to prevent the collection of income in a small capitalist society and to potentially help those who are negatively affected by the automation revolution, robots must be defined as an electronic person and a robot tax is required. [ABSTRACT FROM AUTHOR]

This paper addresses the fault estimation (FE) and accommodation issues of interconnected systems by using two new concepts namely interconnected separation principle and constrained interconnected separation principle that allow for the separate design not only between diagnostic observer and fault tolerant controller for each subsystem, but also between observer/controller of each subsystem and those of other ones. Sufficient fault recoverability conditions are established, under which both distributed and decentralized FE and accommodation schemes are provided. The new results help to provide a framework for observer-based fault diagnosis and fault tolerant control of interconnected systems, and are further applied to the meta aircraft configuration that consists of multiple aircraft joined together to illustrate their efficiency. [ABSTRACT FROM AUTHOR]

A parametric multiobjective design approach based on a proportional-integral (PI) controller and a full-state observer is proposed for output regulation in a multivariable linear system. First, a complete parametric form of the observer-based PI control law is established, which yields a closed-loop system with the desired eigenstructure and ensures that the regulated output asymptotically tracks a given constant signal in the presence of constant but unknown disturbances. All design degrees of freedom are preserved and characterized using a set of parameter vectors. Second, a separation principle of eigenvalue sensitivities is proven, and based on this result, the parameters of the closed-loop system are comprehensively optimized to reduce the eigenvalue sensitivity and the control gain, and also to enhance the tolerance to time-varying disturbances. Finally, the proposed method is applied to attitude control of a flexible spacecraft. Moreover, numerical simulations based on practical engineering parameters are performed to verify the superiority of the proposed method over traditional proportional-integral-derivative (PID) control methods. [ABSTRACT FROM AUTHOR]