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The wide spectrum of recent applications for UAVs imposes further challenges to their abilities and control. This is especially true when operating in harsh and hostile environments where disturbances are huge and actuators are prone to failure. Conventional systems and traditional control techniques are not sufficient for stability and tracking under these circumstances. This paper proposes a unique innovative overactuated quadrotor system that has six DoFs. The vehicle has four rotors and each rotor can tilt independently in the $YZ$-plane. It has the ability to correct its position and attitude in a decoupled way which is different from the conventional quadrotor configurations. Sliding-mode control associated with switching control mode is used for the control algorithm of the system. The system shows agility in the face of large disturbances and robustness against actuator failure which makes it a perfect fit for extreme and challenging environments. The concept of the system and its ability are illustrated in simulation with promising results.

In this paper, we consider a nonlinear control problem for one-dimensional viscous Burgers’ equation associated with a controlled linear heat equation by means of the Hopf–Cole transformation. The control is carried out by the time-dependent intensity of a distributed heat source influencing the heat equation. The set of admissible controls consists of compactly supported $L^{\infty }$ functions. Using the Green’s function approach, we analyze the possibilities of exact and approximate establishment of a given terminal state for the associated nonlinear Burgers’ equation within a desired amount of time. It is shown that the exact controllability of the associated Burgers’ equation and the heat equation are equivalent. Furthermore, sufficient conditions for the approximate controllability are derived. The set of resolving controls is constructed in both cases. The determination of the resolving controls providing exact controllability is reduced to an infinite-dimensional system of linear algebraic equations. By means of the heuristic method of resolving control determination, parametric hierarchies of solutions providing approximate controllability are constructed. The results of a numerical simulation supporting the theoretical derivations are discussed.

In this paper, a novel approach for generating multi-wing chaotic attractors via switching control is proposed. By using a switching controller, multi-wing chaotic attractors can be generated from a double-wing system. The presented method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. Furthermore, the basic dynamical behaviors, including equilibrium points, maximum Lyapunov exponents and bifurcations, are further investigated. An improved module-based unified circuit is designed for realizing 4, 6, 8 and 10-wing chaotic attractors, and the experimental result is also demonstrated, which is consistent with the numerical simulation.

In this paper, a new adaptive switching control scheme is presented to solve control and synchronization problems. Based on Lyapunov stability theory, an adaptive control law is applied to globally stabilize chaotic systems and achieve states synchronization of two chaotic systems whose dynamics are subjected to the system disturbances and/or some unknown parameters. Simulation examples, the chaotic Chen's system and Chua's circuit, are given to show the feasibility and effectiveness of the proposed theory and method.

This paper reports an autonomous-system-based approach for creating compound chaotic attractors from a class of generalized Lorenz systems via switching control. A state variable scale transformation is proposed for these systems to ensure that all attractors have comparable sizes. Coordinate transformation in the z-axis direction is also used, so that every pair of adjacent chaotic attractors have a common connected domain in the same phase space. Then, by switching control, the intended compound chaotic attractors can be generated. A circuit for a compound Lorenz–Chen–Lü chaotic attractor is designed and implemented for demonstration, which verifies the effectiveness of the proposed simulation-based technique. The aim of this report is to demonstrate the possibility of accomplishing such a very challenging task, leaving the extremely difficult underlying theory to future studies.

This paper further investigates a novel method, namely the mirror and double-mirror symmetry conversion both in z direction and in y direction, for generating complex grid multiwing chaotic attractors from a three-dimensional quadratic chaotic system. First, by designing a switching controller with even-symmetry multisegment quadratic function to extend the number of saddle-focus equilibrium points with index 2 in x direction, multiwing chaotic attractors are obtained. Based on this approach, then, different from the methods proposed in the previous literature, by the mirror and double-mirror symmetry conversion with respect to x-axis and y-axis respectively, various intended grid n × m-wing chaotic systems can be obtained. The principle and method for generating grid multiwing are also given. Numerical simulations and circuit realizations have demonstrated the feasibility and effectiveness of the proposed approaches.

In this work, we investigate the generation of multiwing chaotic attractors using integer and fractional order linear differential equation systems with switching controls. Based on the properties of the Chen system and the Lü system, a series of switching control strategies are proposed to link two linearized, integer or fractional order such systems. Numerical simulation results indicate that the controlled systems exhibit a variety of rich dynamical behaviors including multiwing and grid multiwing chaotic attractors.

In this article, we present a systematic approach to design chaos generators using integer order and fractional order differential equation systems. A series of multiwing chaotic attractors and grid multiwing chaotic attractors are obtained using linear integer order differential equation systems with switching controls. The existence of chaotic attractors in the corresponding fractional order differential equation systems is also investigated. We show that, using the nonlinear fractional order differential equation system, or linear fractional order differential equation systems with switching controls, a series of multiwing chaotic attractors can be obtained.

In this article, we investigate the generation of a class of hyperchaotic systems via the Chen chaotic system using both integer order and fractional order differential equation systems. Based on the Chen chaotic system, we designed a system with four nonlinear ordinary differential equations. For different parameter sets, the trajectory of the system may diverge or display a hyperchaotic attractor with double wings. By linearizing the ordinary differential equation system with divergent trajectory and designing proper switching controls, we obtain a chaotic attractor. Similar phenomenon has also been observed in linearizing the hyperchaotic system. The corresponding fractional order systems are also considered. Our investigation indicates that, switching control can be applied to either linearized chaotic or nonchaotic differential equation systems to create chaotic attractor.

By constructing two three-dimensional (3D) rigorous linear systems, a novel switching control approach for generating chaos from two linear systems is presented. Two 3D linear systems without any constant term have only one common equilibrium point that is the origin. By employing an absolute-value switching law, chaos can be generated by switching between two linear systems. Basic dynamical behaviors of the systems are investigated in detail. Numerical examples illustrate the effectiveness of the presented approach.

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

A three-dimensional smooth continuous-time system with a parameter and two quadratic terms is constructed and a spherical attractor is generated. There exist multiple coexisting spherical attractors based on offset boosting. Two classes of switching signals that depend on the time and the state are designed respectively. By employing a parameter switching control technique, multiple spherical attractors can be generated. Simultaneously, complex chaotic attractors can also be generated by designing a state-dependent switching signal. Numerical examples and corresponding simulations show the effectiveness of the switching control technique.

A problem on how to generate chaos from two 3D linear systems via switching control is investigated. Each linear system has the simplest algebraic structure with three parameters. Two basic conditions of all parameters are given. One of two linear systems is stable. The other is unstable. Switching signals of different quadratic surfaces are designed respectively to generate chaotic dynamical behaviors. The constructed quadratic surfaces can be bounded or unbounded. Numerical examples and corresponding simulations verify the feasibility and effectiveness of the designed switching signals of quadratic surfaces for generating chaos.

A novel and unified design approach on higher-dimensional switching chaos generators is derived in this paper. The whole n-dimensional linear space is divided into two parts by a closed hyper-polyhedron. Two higher-dimensional linear systems with the simplest structures as switching chaos generators are designed successfully to generate chaos. State matrix of the first linear system is Hurwitz stable. State matrix of the second linear system is not Hurwitz stable. Chaotic dynamical behaviors take place due to switching two systems. The switching trajectories go through the boundary of the closed hyper-polyhedron endlessly. Moreover, the size of the hyper-polyhedron can determine and control the amplitude of the chaotic signals. Specific numerical examples on four-dimensional, five-dimensional and six-dimensional switching chaos generators are employed, respectively, to illustrate the effectiveness of the novel and advanced approach presented in this paper. The proposed approach can also be applied to designing other switching chaos generators with the higher dimension beyond six.