A general linear quadratic (LQ) optimal control problem, with the dynamic system being governed by a higher-order vector-valued ordinary differential equation and with inequality-constraints on the state vector and/or the control input, is studied. Based on an explicit characterization result, optimal solutions are obtained in closed-form. A constructive method for finding the closed-form optimal solutions is proposed, and two illustrative examples are included
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This paper presents a novel result on the effect of coupling through both analytical and numerical investigations on linearly coupled systems including chaotic and nonchaotic systems. It is found that when a single system has potential of oscillation but is currently in a "marginal" state to produce a limit cycle via Hopf bifurcation due to the change of a parameter, an appropriate coupling strength can excite the potential limit cycle such that the coupled system oscillates synchronously. Similarly, when a stable limit cycle is at the "margin" of a chaotic attractor in a single system, a certain coupling strength can induce the potential chaotic attractor such that the coupled system has a synchronous chaotic behavior. This excitation mechanism is different from the traditional function of coupling in that the latter mainly drives the coupled system to synchronize with the ongoing dynamics of a single system but does not recover its disappearing dynamics. This newly observed synchronization is called coherent synchronization to distinguish it from various common types of synchronization. Several numerical examples are presented for quantitative description of this interesting phenomenon.
This paper reports a sequential design of linearly controlling a three-dimensional (3D) quadratic system to a simple six-dimensional hyperchaotic system with complex dynamics. By adding three linear dynamical controllers, the resulting 6D system has no equilibrium and a hidden attractor, which has four positive Lyapunov exponents (LEs). This paper focuses on the 6D system, to reveal its unusual dynamics such as infinitely many singularly degenerate heteroclinic cycles and bifurcations from such singular orbits to hidden hyperchaotic attractors. Detailed numerical investigations are carried out, including bifurcation diagram, LE spectrum and phase portrait. Furthermore, the system has multistability corresponding to three types of equilibria, including no equilibrium and infinite non-isolated equilibria. In particular, we find that at least seven different attractors coexist when the system has one equilibrium line. Finally, this 6D hyperchaotic system is verified by 0–1 test and a circuit.
In this paper, the problem of making a nonchaotic continuous-time system chaotic via nonlinear time-delay feedback is studied. The designed controller is a combination of a feedback stabilization law and a time-delay feedback law with an arbitrarily small-amplitude, which together can make the system chaotic. An example is included for illustration.
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Drastic reduction in biodiversity has been a severe threat to ecosystems, which is exacerbated when losing few species leads to disastrous and even irreparable consequences. Therefore, revealing the mechanism underlining biodiversity loss is of uttermost importance. In this study, we show that abundant indirect interactions among mutualistic ecosystems are critical in determining species' status. Combining topological and ecological characteristics, we propose an indicator derived from a dynamic model to identify keystone species and quantify their influence, which outperforms widely-used indicators like degree in realistic and simulated networks. Furthermore, we demonstrate that networks with high modularity, heterogeneity, biodiversity, and less intimate interactions tend to have larger indirect effects, which are more amenable in predicting decline of biodiversity with the proposed indicator. These findings shed some light onto the influence of apposite biodiversities, paving the way from complex network theory to ecosystem protection and restoration.
This brief presents some new and explicit stability results for Volterra systems based on two different approaches. The first approach is based on monomial domination of the Volterra system's memoryless output nonlinearity and the second on its Lipschitz-norm. The former yields more widely applicable results, but introduces nonconvexity in the signal spaces to be dealt with for certain parameter values.
In order to further explore the mechanism responsible for weighted complex networks, we introduce a new model that incorporates the network topology and the weights' dynamical evolutions. Our model can capture the details of weight dynamics caused not only by the addition of a new node with new links and new links between old nodes, but also the deletion of old links. We calculate analytically the distributions of both degree and strength and found that all these distributions show scale-free behavior, as confirmed in many real networks. Thus our model characterizes the real weighted complex networks more precisely.
Introduction to Fuzzy Systems provides students with a self-contained introduction that requires no preliminary knowledge of fuzzy mathematics and fuzzy control systems theory. Simplified and readily accessible, it encourages both classroom and self-directed learners to build a solid foundation in fuzzy systems. After introducing the subjec