Showing papers on "Discrete time and continuous time published in 2021"
TL;DR: The proposed design scheme provides an effective way in establishing the relationship between the system states and the controlled errors, by which a noise-intensity-dependant stability condition is derived to ensure that the closed-loop system is exponentially mean-square stable for exactly known systems.
Abstract: This article is concerned with the exponential mean-square stabilization problem for a class of discrete-time strict-feedback nonlinear systems subject to multiplicative noises. The state-dependent multiplicative noise is assumed to occur randomly based on a stochastic variable obeying the Gaussian white distribution. To tackle the difficulties caused by the multiplicative noise, a novel backstepping-based control framework is developed to design both the virtual control laws and the actual control law for the original nonlinear system, and such a framework is fundamentally different from the traditional $n$ -step predictor strategy. The proposed design scheme provides an effective way in establishing the relationship between the system states and the controlled errors, by which a noise-intensity-dependant stability condition is derived to ensure that the closed-loop system is exponentially mean-square stable for exactly known systems. To further cope with nonlinear modeling uncertainties, the radial basis function neural network (NN) is employed as a function approximator. In virtue of the proposed backstepping-based control framework, the ideal controller is characterized as a function of all system states, which is independent of the virtual control laws. Therefore, only one NN is employed in the final step of the backstepping procedure and, subsequently, a novel adaptive neural controller (with modified weight updating laws) is presented to ensure that both the neural weight estimates and the system states are uniformly bounded in the mean-square sense under certain stability conditions. The control performance of the proposed scheme is illustrated through simulation results.
86 citations
TL;DR: In this paper, a unified treatment of the continuous and the discrete-time cases is presented, and two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation.
Abstract: We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include the following, first, a unified treatment of the continuous and the discrete-time cases; second, the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement , and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and, third, an alternative estimator ensuring convergence in finite-time whose adaptation gain, in contrast with the existing one, does not converge to zero. Simulations that illustrate our results are also presented.
64 citations
TL;DR: Improved stability criteria are provided for switched T–S fuzzy systems containing both stable and unstable modes by establishing a semitime-dependent Lyapunov function and exploring the property of mode-dependent average dwell-time switching.
Abstract: This paper concerns with the stability analysis for a class of discrete-time switched Takagi–Sugeno (T–S) fuzzy systems. By establishing a semitime-dependent Lyapunov function and exploring the property of mode-dependent average dwell-time switching, improved stability criteria are provided for switched T–S fuzzy systems containing both stable and unstable modes. Then, slow and fast switching strategies are designed, which are adopted for stable and unstable subsystems, respectively. Especially, we also provide the stability conditions for switched systems with all modes stable and unstable. Finally, the validities and advantages of provided techniques are illustrated by some simulation examples.
64 citations
TL;DR: This work provides a fast algorithm for computing Jacobians for heterogeneous agents, a technique to substantially reduce dimensionality, a rapid procedure for likelihood-based estimation, a determinacy condition for the sequence space, and a method to solve nonlinear perfect-foresight transitions.
Abstract: We propose a general and highly efficient method for solving and estimating general equilibrium heterogeneous-agent models with aggregate shocks in discrete time. Our approach relies on the rapid computation of sequence-space Jacobians—the derivatives of perfect-foresight equilibrium mappings between aggregate sequences around the steady state. Our main contribution is a fast algorithm for calculating Jacobians for a large class of heterogeneous-agent problems. We combine this algorithm with a systematic approach to composing and inverting Jacobians to solve for general equilibrium impulse responses. We obtain a rapid procedure for likelihood-based estimation and computation of nonlinear perfect-foresight transitions. We apply our methods to three canonical heterogeneous-agent models: a neoclassical model, a New Keynesian model with one asset, and a New Keynesian model with two assets.
62 citations
TL;DR: A novel observer-based PID controller is proposed such that the closed-loop system achieves the desired security level and the quadratic cost criterion (QCC) has an upper bound.
Abstract: This article deals with the observer-based proportional-integral-derivative (PID) security control problem for a kind of linear discrete time-delay systems subject to cyber-attacks. The cyber-attacks, which include both denial-of-service and deception attacks, are allowed to be randomly occurring as regulated by two sequences of Bernoulli distributed random variables with certain probabilities. A novel observer-based PID controller is proposed such that the closed-loop system achieves the desired security level and the quadratic cost criterion (QCC) has an upper bound. Sufficient conditions are derived under which the exponentially mean-square input-to-state stability is guaranteed and the desired security level is then achieved. Subsequently, an upper bound of the QCC is obtained and the explicit expression of the desired PID controller is also parameterized. Finally, the validity of the developed design approach is verified via an illustrative example.
60 citations
59 citations
TL;DR: In this article, the data-based two-player zero-sum game problem is considered for linear discrete-time systems and it is proved that the PIQL algorithm is equivalent to the Newton iteration method in the Banach space by using the Fréchet derivative.
Abstract: In this article, the data-based two-player zero-sum game problem is considered for linear discrete-time systems. This problem theoretically depends on solving the discrete-time game algebraic Riccati equation (DTGARE), while it requires complete system dynamics. To avoid solving the DTGARE, the $Q$ -function is introduced and a data-based policy iteration $Q$ -learning (PIQL) algorithm is developed to learn the optimal $Q$ -function by using data collected from the real system. Writing the $Q$ -function in a quadratic form, it is proved that the PIQL algorithm is equivalent to the Newton iteration method in the Banach space by using the Frechet derivative. Then, the convergence of the PIQL algorithm can be guaranteed by Kantorovich’s theorem. For the realization of the PIQL algorithm, the off-policy learning scheme is proposed using real data rather than the system model. Finally, the efficiency of the developed data-based PIQL method is validated through simulation studies.
55 citations
TL;DR: Under the obtained conditions, the filtering error system is exponentially stable and can achieve a weighted $H_\infty$ performance index.
Abstract: This article addresses the $H_\infty$ filtering problem for a class of discrete-time nonlinear switched systems. Every subsystem of the considered nonlinear-switched systems is represented by the Takagi–Sugeno fuzzy systems with local nonlinear models. Signal quantization and filter parameter perturbation are considered simultaneously in the $H_\infty$ filter design. Both the measurement output signal and the performance output signal are quantized by two static quantizers, respectively, before they are transmitted. Based on the average dwell time approach, sufficient conditions for desired $H_\infty$ filters are established in the form of linear matrix inequalities. Under the obtained conditions, the filtering error system is exponentially stable and can achieve a weighted $H_\infty$ performance index. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the obtained results.
51 citations
TL;DR: The discrete time crystal (DTC) is a non-equilibrium phase of matter that spontaneously breaks time-translation symmetry as mentioned in this paper, and disorder-induced many-body localization can stabilize the DTC phase by brea...
Abstract: The discrete time crystal (DTC) is a non-equilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body-localization can stabilize the DTC phase by brea...
50 citations
TL;DR: A fuzzy based-activation feedback controller is proposed for the synchronization of the macroeconomic system and results verify that the proposed control technique can successfully push the states of the response system to the desired value.
Abstract: Economic systems, due to their substantial effects on any society, are interesting research subject for a large family of researchers. Despite all attempts to study economic and financial systems, studies on discrete-time macroeconomic systems are rare. Hence, in the current study, we aim to investigate dynamical behavior and synchronization of these systems. At first, the discrete-time mathematical model of the macroeconomic system is presented. Then, the system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory, which are powerful tools in the investigation of nonlinear systems. This way, the features of the system are disclosed, and the existence of chaos in the system is shown. For the adequate performance of the economy, the economic systems are desired to operate in a unified manner. To this end, in the present research, a fuzzy based-activation feedback controller is proposed for the synchronization of the system. To enhance the celerity and accuracy of the proposed control for synchronization purposes, it is equipped with a fuzzy logic engine. Finally, the numerical simulations of the synchronization are presented and compared with those of a conventional activation feedback control. Numerical results verify that the proposed control technique can successfully push the states of the response system to the desired value.
50 citations
TL;DR: The bipartite tracking consensus for a set of mobile autonomous agents over directed cooperation–competition networks is addressed, here, cooperative and competitive interactions among the agents are described by positive and negative edges of the directed network topology.
Abstract: This article addresses the bipartite tracking consensus for a set of mobile autonomous agents over directed cooperation–competition networks. Here, cooperative and competitive interactions among the agents are described by positive and negative edges of the directed network topology, respectively. Both fixed and switching network topologies are considered. For the case with fixed network topology, the matrix product technique is utilized to derive the convergence result. For the case with switching network topologies, some key results related to the composition of binary relations are the main technical tools of analyzing the error system. In addition, the upper bound for the spectral radius of the system matrix is given to ensure the convergence of the system even if the single uncoupled system is strictly unstable. The applicability of the derived results is verified through two simulation experiments.
TL;DR: This paper provides a novel tool to understand fractional uncertainty problems on discrete time domains by providing exact solutions of two linear equations obtained by Picard's iteration.
TL;DR: A new event-triggered communication scheme, based on designing a virtual system for each agent, is proposed to achieve the coordination task without velocity information to solve the consensus problem of multiple Euler–Lagrange systems subject to unavailable velocity information and limited communication resources.
Abstract: This article considers the consensus problem of multiple Euler–Lagrange systems subject to unavailable velocity information and limited communication resources. First, a new event-triggered communication scheme, based on designing a virtual system for each agent, is proposed to achieve the coordination task without velocity information. The event-triggering conditions only rely on the states of virtual systems and allow agents to transmit virtual states only at some discrete time instants. Under the proposed strategy, the control objective can be accomplished with lower communication and measurement costs. Second, we consider the time delay effects in each information channel with event-triggered communication. For the proposed event-triggered scheme, the Zeno triggering is excluded. Finally, two simulation examples with six two-linked robot manipulator arms are given to demonstrate the effectiveness of the proposed scheme.
TL;DR: In this paper, a data-driven distributed formation control algorithm is proposed for an unknown heterogeneous non-affine nonlinear discrete-time MIMO multi-agent system (MAS) with sensor fault.
Abstract: A data-driven distributed formation control algorithm is proposed for an unknown heterogeneous non-affine nonlinear discrete-time MIMO multi-agent system (MAS) with sensor fault. For the considered unknown MAS, the dynamic linearization technique in model-free adaptive control (MFAC) theory is used to transform the unknown MAS into an equivalent virtual dynamic linearization data model. Then using the virtual data model, the structure of the distributed model-free adaptive controller is constructed. For the incorrect signal measurements due to the sensor fault, the radial basis function neural network (RBFNN) is first trained for the MAS under the fault-free case, then using the outputs of the well-trained RBFNN and the actual outputs of MAS under sensor fault case, the estimation laws of the unknown fault and system parameters in the virtual data model are designed with only the measured input-output (I/O) data information. Finally, the boundedness of the formation error is analyzed by the contraction mapping method and mathematical induction method. The effectiveness of the proposed algorithm is illustrated by simulation examples.
TL;DR: In this paper, a discrete-time version of ETM is proposed, under which the sensors sample the signals in a periodic manner, but whether the sampling signals are transmitted to controllers or not is determined by a predefined periodic ETM.
Abstract: In this article, we investigate the periodic event-triggered synchronization of discrete-time complex dynamical networks (CDNs). First, a discrete-time version of periodic event-triggered mechanism (ETM) is proposed, under which the sensors sample the signals in a periodic manner. But whether the sampling signals are transmitted to controllers or not is determined by a predefined periodic ETM. Compared with the common ETMs in the field of discrete-time systems, the proposed method avoids monitoring the measurements point-to-point and enlarges the lower bound of the inter-event intervals. As a result, it is beneficial to save both the energy and communication resources. Second, the ``discontinuous'' Lyapunov functionals are constructed to deal with the sawtooth constraint of sampling signals. The functionals can be viewed as the discrete-time extension for those discontinuous ones in continuous-time fields. Third, sufficient conditions for the ultimately bounded synchronization are derived for the discrete-time CDNs with or without considering communication delays, respectively. A calculation method for simultaneously designing the triggering parameter and control gains is developed such that the estimation of error level is accurate as much as possible. Finally, the simulation examples are presented to show the effectiveness and improvements of the proposed method.
TL;DR: A mixed H−/H∞ fault-detection filtering is proposed to construct the residual signal and an eventtriggered scenario is recommended to reduce the burden of communication processes by determining whether measurements should be transmitted or not.
Abstract: To improve the safety and reliability of industrial processes, fault-detection problems in dynamic systems have attracted increasing research attention [1]. On the one hand, to enhance fault sensitivity, applying the H− performance index to measure the minimum impact of the fault on the residual signal has been proposed. On the other hand, due to inevitable external disturbances, the fault-detection filter should restrain the impact of interference signals below a prescribed level while detecting faults. Besides, because the network bandwidth of communication is limited, the eventtriggered fault-detection mechanism has been studied extensively to save network resources [2]. The main contributions of this study are as follows: (1) By considering the faults and external disturbances in the model, a mixed H−/H∞ fault-detection filtering is proposed to construct the residual signal. (2) An eventtriggered scenario is recommended to reduce the burden of communication processes by determining whether measurements should be transmitted or not. (3) Based on a new difference operator associated with Lyapunov functions [3, 4], which only depends on the mathematical expectation of white noise {wk}, a more practical result for the H−/H∞ fault detection filter for general nonlinear discrete switched stochastic systems is provided. The notations are provided in Appendix A. Problem description. In this study, we focus on the following discrete-time nonlinear switching stochastic system:
TL;DR: This article develops a novel event-triggered control (ETC) approach based on the deterministic policy gradient (PG) adaptive dynamic programming (ADP) algorithm which updates the control law and the disturbance law with a gradient descent algorithm.
Abstract: In order to address zero-sum game problems for discrete-time (DT) nonlinear systems, this article develops a novel event-triggered control (ETC) approach based on the deterministic policy gradient (PG) adaptive dynamic programming (ADP) algorithm. By adopting the input and output data, the proposed ETC method updates the control law and the disturbance law with a gradient descent algorithm. Compared with the conventional PG ADP-based control scheme, the present controller is updated aperiodically to reduce the computational and communication burden. Then, the actor-critic-disturbance framework is adopted to obtain the optimal control law and the worst disturbance law, which guarantee the input-to-state stability of the closed-loop system. Moreover, a novel neural network weight updating law which guarantees the uniform ultimate boundedness of weight estimation errors is provided based on the experience replay technique. Finally, the validity of the present method is verified by simulation of two DT nonlinear systems.
TL;DR: This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology, and the saturation phenomenon of physical actuators is specifically considered in designing feedback controllers.
Abstract: This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology. The saturation phenomenon of physical actuators is specifically considered in designing feedback controllers. By exploring the mixed-delay-dependent sector conditions in combination with the piecewise Lyapunov-like functional and the average-dwell-time switching, a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances, while the $l_{2}$ – $l_\infty $ performance constraint is satisfied. Furthermore, the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances. Second, by using some congruence transformations, the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities. Then, three convex optimization problems are formulated regarding the disturbance tolerance, the $l_{2}$ – $l_\infty $ performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.
TL;DR: A basic introduction to high-order fully actuated (HOFA) approaches for discrete-time systems for general dynamical disc systems is given.
Abstract: A basic introduction to high-order fully actuated (HOFA) approaches for discrete-time systems is given. Firstly, it is shown that, different from the continuous-time systems, general dynamical disc...
TL;DR: Applying the lexicographical order method to the quaternion-valued memristive neural networks, the closed convex hull consisted by the connection weights is meaningful and one example is given to substantiate the obtained conclusions.
TL;DR: It is shown that with the proposed reset algorithm, the state estimation error is improved in the presence of over or under estimation, and the boundedness of the estimationerror is established.
Abstract: This article addresses reset moving horizon estimation for multiple output discrete-time systems with quantized measurements. A new state reset estimator is designed based on a one-dimensional noisy measurement to overcome underestimation or overestimation of the system state, and an iterative algorithm is proposed to deal with multiple output systems. It is shown that with the proposed reset algorithm, the state estimation error is improved in the presence of over or under estimation, and the boundedness of the estimation error is established. The proposed algorithm also achieves a better estimate than the existing one for systems with a scalar measurement in the static case. A simulation of a moving vehicle is provided to demonstrate the advantage of the developed approach.
22 Jun 2021
TL;DR: In this paper, the exact solutions of equations with GFI and GFD at discrete points were derived for general nonlocal mappings without approximations, where the nonlocality is determined by the operator kernels that belong to the Sonin and Luchko sets of kernel pairs.
Abstract: General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with discrete time. GFDynamics implies research and obtaining results concerning the general form of nonlocality, which can be described by general-form operator kernels and not by its particular implementations and representations. In this paper, the concept of “general nonlocal mappings” is proposed; these are the exact solutions of equations with GFI and GFD at discrete points. In these mappings, the nonlocality is determined by the operator kernels that belong to the Sonin and Luchko sets of kernel pairs. These types of kernels are used in general fractional integrals and derivatives for the initial equations. Using general fractional calculus, we considered fractional systems with general nonlocality in time, which are described by equations with general fractional operators and periodic kicks. Equations with GFI and GFD of arbitrary order were also used to derive general nonlocal mappings. The exact solutions for these general fractional differential and integral equations with kicks were obtained. These exact solutions with discrete timepoints were used to derive general nonlocal mappings without approximations. Some examples of nonlocality in time are described.
TL;DR: In this study, three numerical analysis examples and one engineering design example are presented to demonstrate the effectiveness of the proposed Kriging-assisted time-variant reliability analysis method based upon stochastic process discretization.
TL;DR: A novel polytopic model is first proposed to characterize the delayed saturation nonlinearity of discrete-time systems with both distributed state delay and fast-varying input delay under actuator saturations and a sufficient condition is established by means of linear matrix inequalities under which the closed-loop system is locally exponentially stable.
Abstract: This article is concerned with the local stabilization problem for discrete-time systems with both distributed state delay and fast-varying input delay under actuator saturations. By introducing some terms concerning the distributedly delayed state and the current state, a novel polytopic model is first proposed to characterize the delayed saturation nonlinearity. Then, by incorporating a piecewise Lyapunov functional and some summation inequalities, a sufficient condition is established by means of linear matrix inequalities under which the closed-loop system is locally exponentially stable. Moreover, the conditions for two special cases with single state delay and single input delay are proposed. Subsequently, certain optimization problems are formulated with aim to maximize the estimate of the region of attraction. Finally, two examples show the effectiveness and values of the obtained results.
TL;DR: This novel research introduces for the first time a fractional-calculus based artificial macroeconomic model, actually implemented in the Laboratory via a new hardware set up, and pave the way for future studies on the incorporation of fractional calculus into macroeconomic models.
Abstract: In this novel research, through dynamical analysis, we introduce for the first time a fractional-calculus based artificial macroeconomic model, actually implemented in the Laboratory via a new hardware set up. Firstly, we propose a new model of a discrete-time macroeconomic system where fractional derivatives are incorporated into the system of equations. Using well-known tools and methods, including bifurcation diagrams and Lyapunov exponents, the characteristics of the system are disclosed, and the importance of the fractional-order derivative in the modeling of the system is shown. After that, a laboratory hardware realization is also carried out for the proposed system that provides further insight and a better understanding of the properties of the system. For the hardware realization an Arduino Due™ is chosen in which possess two analog output pins. Experimental results conspicuously illustrate the chaotic behavior of the system. Through the results of the hardware realization, phase portraits and bifurcation diagram of the system are demonstrated, and the effects of the parameters and fractional derivatives are studied. We believe the presented study and its results pave the way for future studies on the incorporation of fractional calculus into macroeconomic models.
TL;DR: In this article, the adaptive control problem for continuous-time nonlinear systems described by differential equations is studied and a learning-based control algorithm is proposed to learn robust optimal controllers directly from real-time data.
Abstract: This article studies the adaptive optimal control problem for continuous-time nonlinear systems described by differential equations. A key strategy is to exploit the value iteration (VI) method proposed initially by Bellman in 1957 as a fundamental tool to solve dynamic programming problems. However, previous VI methods are all exclusively devoted to the Markov decision processes and discrete-time dynamical systems. In this article, we aim to fill up the gap by developing a new continuous-time VI method that will be applied to address the adaptive or nonadaptive optimal control problems for continuous-time systems described by differential equations. Like the traditional VI, the continuous-time VI algorithm retains the nice feature that there is no need to assume the knowledge of an initial admissible control policy. As a direct application of the proposed VI method, a new class of adaptive optimal controllers is obtained for nonlinear systems with totally unknown dynamics. A learning-based control algorithm is proposed to show how to learn robust optimal controllers directly from real-time data. Finally, two examples are given to illustrate the efficacy of the proposed methodology.
TL;DR: This article presents a unified framework for the stability and performance analysis of networked linear control systems with asynchronous continuous-time or discrete-time event-triggering, and characterize the robustness of the system in a time-delayed networked scenario with independent event-triggered sending of each output.
Abstract: This article presents a unified framework for the stability and performance analysis of networked linear control systems with asynchronous continuous-time or discrete-time event-triggering. In the networked system, the multiple outputs of the plant and the controller are independently transmitted via a single shared or multiple channels based on local event-triggering conditions. Regarding the restrictions of physical devices, in the event-checking procedure, an inactive period of time is allowed after each event of data sending. So the Zeno behaviors in events are effectively avoided. In terms of algebraic properties of state-space models and time delays, we present sufficient conditions for asymptotic stability and guaranteed $\mathcal {L}_2$ gain performance and characterize the robustness of the system in a time-delayed networked scenario with independent event-triggered sending of each output. The event-triggered approach provides the potential benefit of reduced number of requests for sending data via networks. A simulation example is given to verify the proposed methods.
TL;DR: In this article, the authors studied discrete space and time first-passage processes under discrete time resetting in a general setup without specifying their forms and sketch out the steps to compute the moments and probability density function which is often intractable in the continuous time restarted process.
Abstract: First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to outperform the completion of many first-passage processes which otherwise would take longer time to finish. However, most of the studies so far assumed continuous time underlying first-passage time processes and moreover considered continuous time resetting restricting out restart processes broken up into synchronized time steps. To bridge this gap, in this paper, we study discrete space and time first-passage processes under discrete time resetting in a general setup without specifying their forms. We sketch out the steps to compute the moments and the probability density function which is often intractable in the continuous time restarted process. A criterion that dictates when restart remains beneficial is then derived. We apply our results to a symmetric and a biased random walker in one-dimensional lattice confined within two absorbing boundaries. Numerical simulations are found to be in excellent agreement with the theoretical results. Our method can be useful to understand the effect of restart on the spatiotemporal dynamics of confined lattice random walks in arbitrary dimensions.
TL;DR: It is proved that minimizers of the fully discrete problem converge to minimizer of the spatially continuous, discrete time problem as the spatial discretization is refined, including higher-order convergence the novel Crank–Nicolson-type method, when compared to the classical JKO method.
Abstract: Combining the classical theory of optimal transport with modern operator splitting techniques, we develop a new numerical method for nonlinear, nonlocal partial differential equations, arising in models of porous media, materials science, and biological swarming. Our method proceeds as follows: first, we discretize in time, either via the classical JKO scheme or via a novel Crank–Nicolson-type method we introduce. Next, we use the Benamou–Brenier dynamical characterization of the Wasserstein distance to reduce computing the solution of the discrete time equations to solving fully discrete minimization problems, with strictly convex objective functions and linear constraints. Third, we compute the minimizers by applying a recently introduced, provably convergent primal dual splitting scheme for three operators (Yan in J Sci Comput 1–20, 2018). By leveraging the PDEs’ underlying variational structure, our method overcomes stability issues present in previous numerical work built on explicit time discretizations, which suffer due to the equations’ strong nonlinearities and degeneracies. Our method is also naturally positivity and mass preserving and, in the case of the JKO scheme, energy decreasing. We prove that minimizers of the fully discrete problem converge to minimizers of the spatially continuous, discrete time problem as the spatial discretization is refined. We conclude with simulations of nonlinear PDEs and Wasserstein geodesics in one and two dimensions that illustrate the key properties of our approach, including higher-order convergence our novel Crank–Nicolson-type method, when compared to the classical JKO method.