The minimum time control problem for a class of non-holonomic controllable nonlinear systems is considered in this paper. These nonlinear systems have drift free dynamics with fewer controls than states. After some re...
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The minimum time control problem for a class of non-holonomic controllable nonlinear systems is considered in this paper. These nonlinear systems have drift free dynamics with fewer controls than states. After some review and preliminar results, it is shown, that in general the problem is not solveable. Next, under some restrictions on the control inputs we are able to characterize the zero crossing set and to get solutlOns which result to be of the bang-bang form. Finally, a case study is presented where the proposed solution is compared with other methodologies which solve the point to point motion planning problem, showing that indeed is the best, one can obtain.
It was shown in [1] that for control-affine nonlinear systems, global asymptotic stabilizability via continuous state feedback implies global input-to-state stabilizability with respect to actuator disturbances. We sh...
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It was shown in [1] that for control-affine nonlinear systems, global asymptotic stabilizability via continuous state feedback implies global input-to-state stabilizability with respect to actuator disturbances. We show that the analogous result for sensor disturbances does not hold: we construct a second-order system which admits a continuous memoryless globally asymptotically stabilizing state feedback controller but for which no such controller can prevent finite escape times from every initial condition in the presence of small sensor disturbances.
For nonlinear systems in extended strict feedback form, where unmeasured states enter linearly, we construct dynamic partial state feedback controllers that achieve the global asymptotic tracking of given reference tr...
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For nonlinear systems in extended strict feedback form, where unmeasured states enter linearly, we construct dynamic partial state feedback controllers that achieve the global asymptotic tracking of given reference trajectories while maintaining internal boundedness.
We develop tools for backstepping with Lyapunov functions and control laws which are locally Lipschitz but not differentiable. We use Clarke’s generalized gradient and its associated calculus to show that the locally...
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We develop tools for backstepping with Lyapunov functions and control laws which are locally Lipschitz but not differentiable. We use Clarke’s generalized gradient and its associated calculus to show that the locally Lipschitz backstepping construction is essentially the same as the differentiable one. Our recursive method is constructive and yields an explicit expression for the control law.
The fidelity of a signal formed by recalling samples of a sinusoid from a look-up table and converting these sample amplitudes to a waveform in a digital-to-analog converter (DAC) is affected by both the phase and amp...
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The misadjustment exhibited by the constant modulus algorithm (CMA) can be excessive when it is used for blind equalization of QAM signals, thus degrading the performance of decision-directed carrier recovery algorith...
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The purpose of this paper is to investigate in an infinite dimensional space, the first passage problem with a risk-sensitive performance criterion, and to illustrate the asymptotic behavior of the associated value fu...
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The purpose of this paper is to investigate in an infinite dimensional space, the first passage problem with a risk-sensitive performance criterion, and to illustrate the asymptotic behavior of the associated value function, as related to differential games arising in robust control theory. The model of interest is described by a controlled stochastic evolution with small Wiener noise intensity. The Wiener and state processes take values in infinite dimensional Hilbert spaces. The objective is to control the evolution of the state process, so as to keep it in some compact set G. By using a logarithmic transformation, it is shown that in the limit as the small noise parameter, /spl epsiv//spl rarr/0, the risk-sensitive value function converges to the value of a deterministic differential game. In the limit as the risk parameter, /spl theta//spl rarr/0, the risk-sensitive value function converges to the value function corresponding to the mean escape time problem. In addition, a lower bound on the first escape time is derived which is slightly different from the known bound for finite dimensional systems. The magnitude of the lower bound derived here, increases as /spl theta/ increases, thus robustness is achieved.
Smart materials such as piezoceramics and shape memory alloys (SMAs) exhibit significant hysteresis and in order to estimate the effect on open and closed loop control a suitable model is needed. One promising candida...
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Smart materials such as piezoceramics and shape memory alloys (SMAs) exhibit significant hysteresis and in order to estimate the effect on open and closed loop control a suitable model is needed. One promising candidate is the Preisach independent domain hysteresis model that is characterized by the congruent minor loop and wiping out properties. Comparable minor loop and decaying oscillation test data for a multi-sheet piezoceramic actuator (made of lead zirconate titanate) attached to a flexible beam are presented and are seen to be very consistent with the two Preisach model properties. The commanded parameter is the sheet transverse electric field while the measured parameter is an approximately colocated strain induced in the beam. Equivalent data for a Nitinol SMA wire muscle, attached to the same beam, are also presented. The input and output parameters are the SMA current and a beam strain respectfully. The minor loop and wiping out evidence is less strong than that of the piezoceramic case, but encouraging. In all experiments the quasi-steady state responses were generated in order to avoid exciting beam flexible modes which would complicate the analysis.
Passivity based controllers are used in structural control due to their inherent robustness properties. These controllers require sensor/actuator collocation. In this paper, we consider the design of a "squaring ...
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Passivity based controllers are used in structural control due to their inherent robustness properties. These controllers require sensor/actuator collocation. In this paper, we consider the design of a "squaring down" matrix which renders a system passive by using a linear combination of all collocated and non-collocated sensor/actuator pairs. The design uses experimental transfer functions and does not require the knowledge of the system model. The problem of finding the squaring down matrix is cast as a solution to a set of linear matrix inequalities (LMIs) subject to some additional performance considerations. The design procedure of the squaring down matrix assumes that velocity information is available from the sensors which is not generally the case. We show that the squaring down matrix can be implemented without the use of such velocity information. We provide experimental results gathered from the single link flexible beam setup in the C/sub La/MS laboratory at RPI to show that implementation of passive loops without velocity measurements provides very good results.
The fidelity of a signal formed by recalling samples of a sinusoid from a look-up table and converting these sample amplitudes to a waveform in a digital-to-analog converter (DAC) is affected by both the phase and amp...
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The fidelity of a signal formed by recalling samples of a sinusoid from a look-up table and converting these sample amplitudes to a waveform in a digital-to-analog converter (DAC) is affected by both the phase and amplitude quantization of the process. The length and width of the look-up table affect the signal's phase angle resolution and the signal's amplitude resolution respectively. These resolution limits are equivalent to time base jitter and to amplitude quantization of the signal and add spectral modulation lines and a white broad-band noise floor to the signal's spectrum. These undesired spectral terms can be controlled by the use of noise shaping to spectrally alter the structure of the quantization noise related to limited table length and width.
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