Showing papers on "Autonomous system (mathematics) published in 2009"
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19 Feb 2009TL;DR: In this paper, a new framework based on matrix theory is proposed to analyze and design cooperative controls for a group of individual dynamical systems whose outputs are sensed by or communicated to others in an intermittent, dynamically changing, and local manner.
Abstract: In this paper, a new framework based on matrix theory is proposed to analyze and design cooperative controls for a group of individual dynamical systems whose outputs are sensed by or communicated to others in an intermittent, dynamically changing, and local manner. In the framework, sensing/communication is described mathematically by a time-varying matrix whose dimension is equal to the number of dynamical systems in the group and whose elements assume piecewise-constant and binary values. Dynamical systems are generally heterogeneous and can be transformed into a canonical form of different, arbitrary, but finite relative degrees. Utilizing a set of new results on augmentation of irreducible matrices and on lower triangulation of reducible matrices, the framework allows a designer to study how a general local-and-output-feedback cooperative control can determine group behaviors of the dynamical systems and to see how changes of sensing/communication would impact the group behaviors over time. A necessary and sufficient condition on convergence of a multiplicative sequence of reducible row-stochastic (diagonally positive) matrices is explicitly derived, and through simple choices of a gain matrix in the cooperative control law, the overall closed-loop system is shown to exhibit cooperative behaviors (such as single group behavior, multiple group behaviors, adaptive cooperative behavior for the group, and cooperative formation including individual behaviors). Examples, including formation control of nonholonomic systems in the chained form, are used to illustrate the proposed framework.
937 citations
TL;DR: The proposed algorithm was at the core of the planning and control software for Team MIT's entry for the 2007 DARPA Urban Challenge, where the vehicle demonstrated the ability to complete a 60 mile simulated military supply mission, while safely interacting with other autonomous and human driven vehicles.
Abstract: This paper describes a real-time motion planning algorithm, based on the rapidly-exploring random tree (RRT) approach, applicable to autonomous vehicles operating in an urban environment. Extensions to the standard RRT are predominantly motivated by: 1) the need to generate dynamically feasible plans in real-time; 2) safety requirements; 3) the constraints dictated by the uncertain operating (urban) environment. The primary novelty is in the use of closed-loop prediction in the framework of RRT. The proposed algorithm was at the core of the planning and control software for Team MIT's entry for the 2007 DARPA Urban Challenge, where the vehicle demonstrated the ability to complete a 60 mile simulated military supply mission, while safely interacting with other autonomous and human driven vehicles.
802 citations
TL;DR: One of the first trials of autonomous intervention performed by SAUVIM in the oceanic environment is described, which consists in a sequence of autonomous tasks finalized to search for the target and to securely hook a cable to it in order to bring the target to the surface.
307 citations
TL;DR: Practical experiments obtained using an autonomous ldquoMini-Bajardquo vehicle equipped with an embedded computing system confirm that the proposed MPC structure is the solution that better matches the target criteria.
Abstract: This paper presents a model predictive controller (MPC) structure for solving the path-tracking problem of terrestrial autonomous vehicles. To achieve the desired performance during high-speed driving, the controller architecture considers both the kinematic and the dynamic control in a cascade structure. Our study contains a comparative study between two kinematic linear predictive control strategies: The first strategy is based on the successive linearization concept, and the other strategy combines a local reference frame with an approaching path strategy. Our goal is to search for the strategy that best comprises the performance and hardware-cost criteria. For the dynamic controller, a decentralized predictive controller based on a linearized model of the vehicle is used. Practical experiments obtained using an autonomous ldquoMini-Bajardquo vehicle equipped with an embedded computing system are presented. These results confirm that the proposed MPC structure is the solution that better matches the target criteria.
266 citations
TL;DR: In this paper, the authors describe the current developments of a class of low-cost, light-weight autonomous underwater vehicles for coastal oceanographic applications; the vehicle class is named Folaga, the Italian name of an aquatic bird that swims on the water surface and dives to catch fish.
157 citations
TL;DR: Boss, the autonomous vehicle that won the DARPA Urban Challenge, is introduced, the complex artificially intelligent software system embodied in a 2007 Chevy Tahoe that builds a model of the world around it in real time.
Abstract: The DARPA Urban Challenge was a competition to develop autonomous vehicles capable of safely, reliably and robustly driving in traffic. In this article we introduce Boss, the autonomous vehicle that won the challenge. Boss is complex artificially intelligent software system embodied in a 2007 Chevy Tahoe. To navigate safely, the vehicle builds a model of the world around it in real time. This model is used to generate safe routes and motion plans in both on roads and in unstructured zones. An essential part of Boss’ success stems from its ability to safely handle both abnormal situations and system glitches.
119 citations
TL;DR: In this article, a new chaotic system of 3-dimensional quadratic autonomous ordinary differential equations was introduced, which can display 2-scroll chaotic attractors and showed that the chaotic system can generate complex 3-scroll and 4-scroll attractors.
Abstract: This article introduces a new chaotic system of 3-D quadratic autonomous ordinary differential equations, which can display 2-scroll chaotic attractors. Some basic dynamical behaviors of the new 3-D system are investigated. Of particular interest is that the chaotic system can generate complex 3-scroll and 4-scroll chaotic attractors. Finally, bifurcation analysis shows that the system can display extremely rich dynamics. The obtained results clearly show that this is a new chaotic system which deserves further detailed investigation.
88 citations
TL;DR: In this paper, the existence of a pullback attractor for a given class D of families of time varying subsets of the phase space is established under minimal assumptions, and under a simple assumption these two notions of attractors generate, in fact, the same object.
Abstract: For an abstract dynamical system, we establish, under minimal assumptions, the existence of D -attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefulness in order to ensure the existence of this last attractor in particular situations. Moreover, we prove that under a simple assumption these two notions of attractors generate, in fact, the same object. This is then applied to a Navier–Stokes model, improving some previous results on attractor theory.
75 citations
TL;DR: Autonomous robots are complex systems that require the interaction or cooperation of numerous heterogeneous software components and are becoming critical systems that must meet safety properties including logical, temporal, and real-time constraints.
Abstract: Autonomous robots are complex systems that require the interaction or cooperation of numerous heterogeneous software components. Nowadays, robots are getting closer to humans and as such are becoming critical systems that must meet safety properties including logical, temporal, and real-time constraints.
66 citations
TL;DR: The paper addresses the problem of bottom-following for autonomous underwater vehicles by taking into account the terrain characteristics ahead of the vehicle, as measured by two echo sounders, using the D-methodology.
Abstract: This paper describes a solution to the problem of bottom-following for autonomous underwater vehicles (AUVs) that relies on the evaluation of the terrain characteristics ahead of the vehicle using echo sounders. The methodology used poses the problem as a discrete time path following control problem where a conveniently defined error state space model of the plant is augmented with bathymetric (i.e., depth) preview data. A piecewise affine parameter-dependent model representation is adopted that describes the AUV linearized error dynamics for a predefined set of operating regions. For each region, a state feedback H 2 control problem for affine parameter-dependent systems is posed and solved using linear matrix inequalities (LMIs). The resulting nonlinear controller is implemented as a gain-scheduled controller using the D-methodology. Simulation results obtained with a nonlinear dynamic model of the INFANTE AUV in the vertical plane are presented and discussed.
63 citations
TL;DR: This work considers the problem of generating optimal trajectories for generic autonomous vehicles and applies pseudospectral methods to develop motion planning algorithms for autonomous vehicles characterized by nonlinear dynamical constraints, an obstacle-cluttered environment, and a need to generate solutions in real time.
Abstract: A COMMON task for autonomous vehicles is motion planning. Discipline-based design of motion planning algorithms have led to the development and evolution of different techniques to solve specific problems. For instance, the artificial–potential–function technique [1] is a popular method for the motion planning of unmanned ground vehicles (UGV) and robotic manipulators [1–3]. Although this technique has been used for over 30 years, it suffers from the possibility of the vehicle not achieving its goal and difficulties in accommodating various environmental constraints [4]. To overcome such issues, recent developments in motion planning algorithms place heavy emphasis on so-called sampling-based planning techniques such as probabilistic road maps, rapidly exploring random trees, and expansive space trees to name a few [5– 9]. These methods use probabilistic means of connecting the initial configuration to thefinal configuration thereby enabling an improved capacity to achieve the goal and a capability to generate initial feasible paths. In all these techniques, the initial feasible paths do not automatically incorporate vehicle dynamics; hence, path-following control techniques are needed to satisfy the physics of themotion [9]. This is one reason why nonholonomic constraints play such a crucial role in constrained control techniques that are designed to serve pathfollowing systems. There is no doubt that optimal control theory is the most natural framework for solving motion planning problems; however, solving optimal control problems has historically been considered difficult due to the twin curses of dimensionality and complexity. These difficulties are exacerbated in the presence of state constraints; hence, an obstacle-cluttered environment becomes a substantially more difficult problem under the framework of optimal control theory [10,11]. Nonetheless, it is possible to solve simplified motion planning problems wherein the cost function is quadratic or the environment is obstacle free. Because the motion planning techniques developed in robotics applications are unsuitable for flight vehicles, such as launch and reentry, for example, aerospace problems have motivated the development of efficient optimal control algorithms. In aerospace applications, satisfaction of the dynamical constraints is exceedingly important; hence, trajectory and control become fundamentally intertwined. On the other hand, aerospace problems do not have the vast number of path constraints that are common in an obstacle-cluttered environment. In recent years, paradigm-changing advancements have taken place in computational optimal control that challenge conventional wisdom. For instance, onboard the International Space Station, Bedrossian et al. [12] discovered and implemented a revolutionary momentum-dumping approach that they call a zero-propellant maneuver. This discovery was made possible by an application of pseudospectral methods to solve a real-life challenging optimal control problem [13]. Other applications of such advancements are discussed in [14,15] and include the ground test of a revolutionary attitude control concept for the NPSAT1 spacecraft. Motivated by these advancements, we apply pseudospectral methods to develop motion planning algorithms for autonomous vehicles characterized by nonlinear dynamical constraints, an obstacle-cluttered environment, and a need to generate solutions in real time. We consider the problem of generating optimal trajectories for generic autonomous vehicles. Shapes of arbitrary number, size, and configuration are modeled in the form of path constraints in the resulting optimal control problem. The method is tested under various obstacle environments on different platforms such as sea surface vehicles, ground vehicles, and aerial vehicles. The optimality of the computed trajectories is verified by way of the necessary conditions. We show that it is possible to do motion planning for different problems under the unified framework of optimal control and pseudospectral methods [16–19].
TL;DR: An on-line, Newton-like optimization algorithm is proposed that recomputes the control variable by attempting to optimize the cost-to-go at equally-spaced epochs and can vary from sublinear to quadratic depending on its computing rate and the state estimation error.
Abstract: This paper considers an optimization problem in the setting of switched-mode hybrid dynamical systems, where the control variable (independent variable) consists of the mode-switching times, and the performance criterion is a cost functional defined on the system's state trajectory. The system is deterministic, nonlinear, and autonomous, and its state variable cannot be measured and hence it has to be estimated. We propose an on-line, Newton-like optimization algorithm that recomputes the control variable by attempting to optimize the cost-to-go at equally-spaced epochs. The main result concerns the algorithm's convergence rate, which can vary from sublinear to quadratic depending on its computing rate and the state estimation error.
01 Jan 2009
TL;DR: This paper reports on AnnieWAY, an autonomous vehicle that is capable of driving through urban scenarios and that has successfully entered the finals of the 2007 DARPA Urban Challenge competition.
Abstract: This paper reports on AnnieWAY, an autonomous vehicle that is capable of driving through urban scenarios and that has successfully entered the finals of the 2007 DARPA Urban Challenge competition. After describing the main challenges imposed and the major hardware components, we outline the underlying software structure and focus on selected algorithms. Environmental perception mainly relies on a recent laser scanner which delivers both range and reflectivity measurements. While range measurements are used to provide 3D scene geometry, measuring reflectivity allows for robust lane marker detection. Mission and maneuver planning is conducted using a concurrent hierarchical state machine that generates behavior in accordance with California traffic laws. We conclude with a report of the results achieved during the competition.
TL;DR: The presented autonomous sensor system, with low-power electronics for radio-frequency (RF) communication, incorporating a thermoelectric energy-harvesting module for unattended operation, can be effectively used for measurements into a close environment in which a temperature difference is present.
Abstract: In this paper, an autonomous sensor system, with low-power electronics for radio-frequency (RF) communication, incorporating a thermoelectric energy-harvesting module for unattended operation is presented A target application is proposed for temperature measurement of walled-in pipes When the autonomous sensor is placed on the heat source, a thermoelectric module harvests energy, powering the autonomous sensor In this condition, no external power source is necessary, the temperature measurement is performed, and the data are saved into a nonvolatile memory When the external readout unit is active, the electromagnetic field is used to power the autonomous sensor system and to communicate the data An experimental setup has been arranged and characterized by measuring the temperature along the pipe, the voltage that can be generated by thermoelectric generators, and the influence of different materials on RF communication The temperature data of the heat source, which are collected by the autonomous sensor, are compared with that of a reference thermistor The measurement results show good agreement between the two measured temperature data sets The experimental data demonstrate that the autonomous system works correctly for a temperature gradient that is higher than 9degC, within a readout distance of a few centimeters The presented autonomous sensor system can be effectively used for measurements into a close environment in which a temperature difference is present
01 Jan 2009
TL;DR: The Boeing VSTL design and capabilities, including the indoor localization system, multi-vehicle command and control (C2) and operator interface, realtime virtual environment, and health-based adaptive behaviors are discussed.
Abstract: Increased levels of vehicle collaboration and auton omy are seen as a means to reduce overall mission completion costs while expanding mi ssion capabilities and increasing mission assurance for complex coupled system of systems. Systems health management technologies have made rapid advances that enable systems to know their own condition and capabilities, thus creating the opportunity for unprecedented lev els of adaptive control, real-time reconfiguration, and mission contingency management. Multi-agent task allocation and mission managements systems must account for vehicle- and system-level health-related issues to ensure that these systems are reliable an d cost effective to operate. Boeing’s Vehicle Swarm Technology Lab (VSTL), established in 2004, includes a 100’x50’x20’ testbed equipped with a vision-based motion capture indoor localization system. The testbed provides a cost-effective rapid prototyping capabil ity for integrating health-based adaptive control of subsystems, vehicle, mission, and swarms to guarantee top-level system-of-systems performance metrics. The lab’s heterogeneous fleet includes over 20 heterogeneous air vehicles, including VTOL and fixed wing, along with their ground stations and communication links in addition to heterogeneous ground vehicles and wall climbing robots. This paper discusses the Boeing VSTL design and capabilities, including the indoor localization system, multi-vehicle command and control (C2) and operator interface, realtime virtual environment, and health-based adaptive behaviors. The lab supports rapid prototyping and exploration of various multi-vehicl e operational concept of operations and missions including persistent surveillance, area se arch and tracking, and high density air traffic management. Additionally, the lab supports experimentation tasks for many other platform configuration and collaborative air, groun d, space, and maritime autonomous system of systems concepts.
TL;DR: TanDEM-X Autonomous Formation Flying performed using a hardware-in-the-loop testbed shows that control performance at the meter level is expected as discussed by the authors, which requires a simple, resource-sparing and robust design of the system.
Abstract: two spacecraft flying on near-circular orbits. Emphasis is given to the practical implementation within an onboard embedded computer, which requires a simple, resource-sparing, and robust design of the system. Therefore, the algorithms are tailored to minimize the usage of onboard resources and to allow the harmonious integration of the relative control system within the space segment. The validation of TanDEM-X Autonomous Formation Flying performed using a hardware-in-the-loop testbed shows that control performance at the meter level is expected.
TL;DR: In this article, a new Lorenz-like chaotic system is reported, where nonlinear characteristic and basic dynamic properties of the three-dimensional autonomous system are studied by means of nonlinear dynamics theory.
Abstract: In this paper, a new Lorenz-like chaotic system is reported. Nonlinear characteristic and basic dynamic properties of the three-dimensional autonomous system are studied by means of nonlinear dynamics theory. The chaotic system is not only demonstrated by theoretical analysis and numerical simulation, such as equilibria stability analysis, Lyapunov-exponent spectra, Lyapunov dimension, bifurcation diagrams, but also implemented via an electronic circuit.
TL;DR: A predictive approach for autonomous navigation that incorporates the shortest path, obstacle avoidance, and uncertainties in sensors and actuators is presented and the capability of avoiding obstacles as well as of approaching a goal is demonstrated.
Abstract: A key feature of an autonomous vehicle is the ability to re-plan its motion from a starting configuration (position and orientation) to a goal configuration while avoiding obstacles. Moreover, it should react robustly to uncertainties throughout its maneuvers. We present a predictive approach for autonomous navigation that incorporates the shortest path, obstacle avoidance, and uncertainties in sensors and actuators. A car-like robot is considered as the autonomous vehicle with nonholonomic and minimum turning radius constraints. The results (arcs and line segments) from a shortest-path planner are used as a reference to find action sequence candidates. The vehicle’s states and their corresponding probability distributions are predicted to determine a future reward value for each action sequence candidate. Finally, an optimal action policy is calculated by maximizing an objective function. Through simulations, the proposed method demonstrates the capability of avoiding obstacles as well as of approaching a goal. The regenerated path will incorporate uncertainty information.
TL;DR: Existence of a quasi-minimal set is proved and an appropriate simulation of a chaotic attractor is presented for a nonautonomous differential equation with a pulse function, whose moments of discontinuity depend on the initial moment.
Abstract: We address a nonautonomous differential equation with a pulse function, whose moments of discontinuity depend on the initial moment. Existence of a quasi-minimal set is proved. An appropriate simulation of a chaotic attractor is presented.
TL;DR: In this paper, the authors propose a methodology for system specification that consists of a notational part, a procedure model and a software tool, covering a substantial part of the overall system engineering process.
Abstract: Today enterprises are exposed to an increasingly dynamic environment. Last but not least increasing competition caused by globalization more and more requires gaining competitive advantages by improved process control, within and beyond an enterprise. Autonomous control of logistic processes is proposed as a means to better face dynamics and complexity. Autonomous control means the ability of logistic objects to process information, to render and to execute decisions on their own. To engineer logistic systems based on autonomous control, dedicated methodologies are needed. This paper proposes a methodology for system specification that consists of a notational part, a procedure model and a software tool, covering a substantial part of the overall system engineering process. Supported by this methodology a logistics process expert will be able to specify an autonomous logistic system adequately. Further research will later on complement the methodology to support the whole engineering process.
TL;DR: In this article, a 3D continuous autonomous system is proposed based on these features, which can generate a four-wing chaotic attractor with less terms in the system equations, and several basic properties of the new system are analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincare maps.
Abstract: In this paper, several three dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have a number of similar features. A new 3-D continuous autonomous system is proposed based on these features. The new system can generate a four-wing chaotic attractor with less terms in the system equations. Several basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincare maps. Phase diagrams show that the equilibria are related to the existence of multiple wings.
TL;DR: A method for designing the dynamic properties of production networks with large numbers of autonomous work systems and a method for distributed computation and communication of information needed to locally compensate for the expected order flows from other work systems are presented.
25 Sep 2009
TL;DR: In this paper, the authors present an on-line trajectory generation method for autonomous overtaking capable of handling emergency situations and aborting the manoeuvre, if required, in a smooth and collision free manner.
Abstract: In the context of intelligent transportation, this paper presents a novel on-line trajectory-generation method for autonomous overtaking capable of handling emergency situations and aborting the manoeuvre, if required, in a smooth and collision free manner. The proposed methodology is guidance based, real-time applicable, and ensures safety and passenger ride comfort. Based on the principles of Rendezvous Guidance, the passing vehicle is guided in real-time to match the position and velocity of a shadow target (i.e., rendezvous with) during the overtaking manoeuvre. The shadow target's position and velocity are generated based on real-time sensory information gathered about the slower vehicle ahead of the passing vehicle. The proposed method can be used as a fully autonomous system or simply as a driver-assistance tool. Extensive simulations, some of which are presented herein, clearly demonstrate the tangible efficiency of the proposed method.
TL;DR: Numerical bifurcation analysis shows that the new 3D quadratic autonomous chaotic system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a flxed point as the proper parameter varies.
Abstract: This paper presents a new 3D quadratic autonomous chaotic system which contains flve system parameters and three quadratic cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a flxed point as the proper parameter varies. Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verifled by the analog circuit realization.
23 Mar 2009
TL;DR: In this paper, the development and building of a fully functioning test bed UAV platform is illustrated, which includes an enhanced hardware in the loop simulation (HILS) system to facilitate the development of the flight control system.
Abstract: Automatic control of Unmanned Aerial Vehicles (UAVs) has been a growing area of research in aerospace technology for a long time, yet this area needs a great deal of development in order to get a reliable autonomous system capable of performing all types of maneuvers with high degree of stability and desired performance. In this paper, the development and building of a fully functioning test bed UAV platform is illustrated. The test-bed includes an enhanced hardware in the loop simulation “HILS” system to facilitate the development of the flight control system (FCS). Furthermore, the design of the guidance laws, autopilots implementation on the embedded system were integrated with the Hardware in the Loop Simulation (HILS). Finally, trajectory following results were demonstrated.
TL;DR: In this article, the authors considered the Lyapunov characteristic spectrum of an ergodic autonomous ODE on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ℝ d.
Abstract: In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ℝ d , not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.
23 Mar 2009
TL;DR: This paper proposes the use of an Agent based computing platform to solve orbit dynamics problems leading to a highly mobile and decentralized system.
Abstract: Space and satellite systems are considered to be the most extreme environment to design for and are fraught with engineering difficulty. Performance metrics such as fault tolerance, reliability, pre-determinism and heritage are still high of the list of requirements for all missions. But with the advent of modern day electronics, greater computing capability and networking technologies have enabled research into distributed satellite systems, where multiple spacecraft work collaboratively to perform a mission. Leveraging from these technologies, a satellite can be considered one of many nodes in an autonomous system. This paper proposes the use of an Agent based computing platform to solve orbit dynamics problems leading to a highly mobile and decentralized system. The latest Agent platforms are compared and possible Agent applications are presented; specifically, distributed image compression and a novel topology reconfiguration scheme.
TL;DR: One approach to designing an optimal real-time collision-free trajectory for autonomous underwater vehicles (AUVs) that move in a 3D unknown underwater space is presented here, and is shown to be effective by computer simulations.
Abstract: One approach to designing an optimal real-time collision-free trajectory for autonomous underwater vehicles (AUVs) that move in a 3D unknown underwater space presented here. By explicitly considering the kinematic model of AUVs, a class of feasible trajectories is derived in a closed form, and is expressed in terms of two adjustable parameters for the purpose of collision avoidance. Then, a collision avoidance condition is developed to determine a class of collision-free trajectories. Finally, a performance index is established to find an optimal trajectory from the class. All the steps can be implemented in real-time. The advantages of the proposed approach are: (1) The 3D motion planning problem is reduced to a 2D problem. Instead of directly searching in a 3D space, one only needs to determine two parameters in their plane. Therefore computational efforts are greatly reduced, which is suitable for real-time implementation; (2) The vehicle's kinematic model is explicitly considered, and all boundary conditions are met. After the parameters are determined, the trajectory and controls are explicitly solved in closed forms. This method is shown to be effective by computer simulations.
TL;DR: In this article, an autonomous system of ODEs solved for the derivatives is considered and its formal and analytical integrals near its finite stationary point are sought from its normal form.
Abstract: We consider an autonomous system of ordinary differential equations (ODEs) solved for the derivatives. Its formal and analytical integrals near its finite stationary point are sought from its normal form. A stationary point at infinity is first mapped to a finite point by a power transformation. This approach is applied to the Yang‐Mills system. It is found that, in the neighborhood of one stationary point at infinity, this system is locally nonintegrable, which supports the well-known result about its global nonintegrability. 1. Consider the autonomous system of ordinary differential equations (1)
TL;DR: An approach to control this novel attractor by non-linear feedback functions is proposed and the results obtained reveal that the trajectories of the chaotic attractor can be controlled to reach certain target periodic orbits or points.
Abstract: From the classical Lu chaotic system a new simple three-dimensional autonomous system is derived, which exhibits a three-scroll chaotic attractor. An approach to control this novel attractor by non-linear feedback functions is proposed. The results obtained reveal that the trajectories of the chaotic attractor can be controlled to reach certain target periodic orbits or points. Finally, some numerical simulations are provided to show the effectiveness and feasibility of the controller design method developed.